### Assuntos

spatial equilibrium models ricardian equivalence ("tax now" or "tax later")

### Papers

Parker, D., Berger, T. and Manson, S., editors. 2002. Agent-based models of land-use and land-cover change. LUCC Report Series, 6, Indiana University.

Petit, O. 2001. Combining mas with gis: Another way to "pixelise" the commons? The Common Property Resource Digest. Quaterly Publication of the international association for the study of common property:9-11.

Röling, N. 1999. Modelling the soft side of the land: The potential of multi-agent systems. Pages 73-97 in C. Leeuwis, editor. Integral design: Innovation in agriculture and resource management. Mansholt Instituu te, Wageningen.

Mertens and Lambin, 2000. land cover-change trajectories in southern cameroon. annals of the association of american geographers, 93, 467-494. (um modelo economico)

#### Generating and Solving Imperfect Information Games

*Work on game playing in AI has typically ignored games of imperfect information such as poker. In
this paper, we present a framework for dealing with such games. We point out several important issues
that arise only in the context of imperfect information games, particularly the insufficiency of a
simple game tree model to represent the players’ information state and the need for randomization in
the players’ optimal strategies. We describe Gala, an implemented system that provides the user with a
very natural and expressive language for describing games. From a game description, Gala creates an
augmented game tree with information sets which can be used by various algorithms in order to find
optimal strategies for that game. In particular, Gala implements the first practical algorithm for finding
optimal randomized strategies in two-player imperfect information competitive games [Koller et al.,
1994]. The running time of this algorithm is polynomial in the size of the game tree, whereas previous
algorithms were exponential. We present experimental results showing that this algorithm is also
efficient in practice and can therefore form the basis for a game playing system.*

#### Evolution of cooperation: cooperation defeats defection in the cornfield model

J. H. Koeslag and E. Terblanche, 2003

*‘‘Cooperation’’ defines any behavior that enhances the fitness of a group (e.g. a community or species), but which, by its nature, can be exploited by selfish individuals, meaning, firstly, that selfish individuals derive an advantage from exploitation which is greater than the average advantage that accrues to unselfish individuals. Secondly, exploitation has no intrinsic fitness value except in the presence of the ‘‘cooperative behavior’’. The mathematics is described by the simple Prisoner’s Dilemma Game (PDG). It has previously been shown that koinophilia (the avoidance of sexual mates displaying unusual or atypical phenotypic features, such as mutations) stabilizes any inherited strategy in the simple or iterated PDG, meaning that it cannot be displaced by rare formsof alternative behavior which arise through mutation or occasional migration. In the present model equal numbersof cooperatorsand defectors(in the simple PDG) were randomly spread in a two-dimensional ‘‘cornfield’’ with uniformly distributed resources. Every individual was koinophilic, and interacted (sexually and in the PDG tournaments) only with individuals from within its immediate neighborhood. This model therefore tested whether cooperation can outcompete defection or selfishness in a straight, initially equally matched, evolutionary battle. The results show that in the absence of koinophilia cooperation was rapidly driven to extinction. With koinophilia there was a very rapid loss of cooperators in the first few generations, but thereafter cooperation slowly spread, ultimately eliminating defection completely. This result was critically dependent on sampling effects of neighborhoods. Small samples (resulting from low population densities or small neighborhood sizes) increase the probability that a chance neighborhood comes to consist predominantly of cooperators. A sexual preference for the most common phenotype in the neighborhood then makes that phenotype more common still. Once this occurs cooperation’s spread becomes almost inevitable.*

#### Social choice and electoral competition in the general spatial model

J. S. Banksa and J. Dugganb and M. Bretond, 2004

*This paper extends the theory of the core, the uncovered set, and the related undominated set to
a general set of alternatives and an arbitrary measure space of voters. We investigate the properties
of social preferences generated by simple games; we extend results on generic emptiness of the
core; we prove the general nonemptiness of the uncovered and undominated sets; and we prove the
upper hemicontinuity of these correspondences when the voters’ preferences are such that the core
is nonempty and externally stable. Finally, we give conditions under which the undominated set is
lower hemicontinuous.*

#### On Spatial Asymmetric Games

E. Ahmed and A. S. Hegazi and A. S. Elgazzar, 2002

*The stability of some spatial asymmetric games is discussed. Both
linear and nonlinear asymptotic stability of asymmetric hawk-dove
and prisoner’s dilemma are studied. Telegraph reaction diffusion equa-
tions for the asymmetric spatial games are presented. Asymmetric
game of parental investment is studied in the presence of both ordi-
nary and cross diffusions.*

#### The evolution of n-player cooperation-threshold games and ESS bifurcations

L. A. Bach and T. Helvik and F. B. Christiansen, 2006

*An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an
n-player Prisioner's Dilemma game. With reference to biological situations, such as group foraging, we
introduce a threshold condition in the number of cooperators required to obtain the collective benefit.
In the simplest version, a three player game, complex behaviour appears as the replicator dynamics exhibits a
catastrophic event separating a parameter region allowing for cohexistence of cooperators and defectors and a
region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond
a critical point in defecting populations. The results illustrate the qualitative difference between two
player games and multiple player games and thus the limitations to the generality of conclusions from two-player
games. We present a procedure to find the ESS in any n-player game with cost and benefit depending on the number
of cooperators. This was previously done by Motro in the special cases of convex and concave benefit functions and
constant cost.*

#### Spatial evolution of automata in the prisoners’ dilemma

*We apply the idea of evolution to a spatial model. Prisoners’ dilemmas or coordination games
are played repeatedly within neighbourhoods where players do not optimise but instead copy successful
strategies. Discriminative behaviour of players is introduced representing strategies as small
automata, which can be in different states against different neighbours. Extensive simulations show
that cooperation persists even in a stochastic environment, that players do not always coordinate
on risk dominant equilibria in 2x2 coordination games, and that success among surviving strategies
may differ. We present two analytical models that help understanding of these phenomena.*

#### The Adaptive Dynamics of Altruism in Spatially Heterogeneous Populations

J. Galliard and R. Ferriere and U. Dieckmann, 2003

*We study the spatial adaptive dynamics of a continuous trait that measures individual investment in altruism.
Our study is based on an ecological model of a spatially heterogeneous population from which we derive an appropriate
measure of fitness. The analysis of this fitness measure uncovers three different selective processes controlling the
evolution of altruism: the direct physiological cost, the indirect genetic benefits of cooperative interactions, and the
indirect genetic costs of competition for space. In our model, habitat structure and a continuous life cycle makes the
cost of competing for space with relatives negligible. Our study yields a classification of adaptive patterns of altruism according to the shape of the costs of altruism (with decelerating, linear, or accelerating dependence on the investment in altruism). The invasion of altruism occurs readily in species with accelerating costs, but large mutations are critical for altruism to evolve in selfish species with decelerating costs. Strict selfishness is maintained by natural selection only under very restricted conditions. In species with rapidly accelerating costs, adaptation leads to an evolutionarily stable rate of investment in altruism that decreases smoothly with the level of mobility. A rather different adaptive pattern emerges in species with slowly accelerating costs: high altruism evolves at low mobility, whereas a quasiselfish state is promoted in more mobile species. The high adaptive level of altruism can be predicted solely from habitat connectedness and physiological parameters that characterize the pattern of cost. We also show that environmental changes that cause increased mobility in those highly altruistic species can beget selection-driven self-extinction, which may contribute to the rarity of social species. *

#### Swarming methods for geospatial reasoning

H V. D. Parunak and S. A. Brueckner and R. Matthews and J. Sauter, 2006

*Geospatial data are often used to predict or recommend movements of robots,
people, or animals (‘walkers’). Analysis of such systems can be combinatorially
explosive. Each decision that a walker makes generates a new set of possible
future decisions, and the tree of possible futures grows exponentially. Complete
enumeration of alternatives is out of the question. One approach that we have
found promising is to instantiate a large population of simple computer agents
that explore possible paths through the landscape. The aggregate behaviour of
this swarm of agents estimates the likely behaviour of the real-world system. This
paper will discuss techniques that we have found useful in swarming geospatial
reasoning, illustrate their behaviour in specific cases, compare them with existing
techniques for path planning, and discuss the application of such systems.*

#### A probe mechanism to couple spatially explicit agents and landscape models in an integrated modelling framework

P. A. Graniero and V. B. Robinson, 2006

*Many environmental, ecological, and social problems require investigation using
a mixture of landscape models, individual-based models, and some level of
interaction between them. Few simulation-modelling frameworks are structured
to handle both styles of model in an integrated fashion. ECO-COSM is a
framework that is capable of handling complex models with both landscape and
agent components. Its Probe-based architecture allows model components to
have controlled access to the state of other components. The ProbeWrapper is a
modification of this common design approach which allows alterations to the
state retrieved from the model and is a critical component of ECO-COSM’s
broad modelling capability. It allows agents to apply perceptual filters or
measurement errors to their observations of the landscape, or apply decisionmaking
strategies in the face of incomplete or uncertain observations. ECOCOSM
is demonstrated with a landscape model of metapopulation dynamics, an
agent model of squirrel dispersal, and a coupled landscape-agent model to
evaluate field-data-acquisition strategies for identifying nutrient or contaminant
hotspots.*

Border topology: wrapping, reflecting or hard (default?)

#### The consequences of labour mobility for redistribution: tax vs. transfer competition

*In a context where both the poor and the rich are (imperfectly) mobile, this paper
compares the Nash equilibrium levels of income redistribution from the rich to the poor
when jurisdictions compete either in taxes, in transfers or both in taxes and transfers.
Although taxes and transfers are linked through the budgetbalanced
requirement, the
analysis reveals intriguing differences. Indeed, it turns out that transfer competition
results in much less redistribution than tax competition, while taxtransfer
competition
involves an intermediate level of redistribution. In each approach, the mobility of the
rich is detrimental to redistribution and an increase in the dependency ratio reduces
taxes. Concerning the effect of the mobility of the poor, these approaches reach opposite
conclusions. That is, the mobility of the poor is beneficial to redistribution under tax
competition but reduces redistribution under transfer competition.*

#### Efficient Nash equilibria in a federal economy with migration costs

G. M. Myers and Y. Y. Papageorgiou, 1997

*We consider a federation of two regions populated by identical individuals, in which
interregional migration is costly. We define a federation as an economy in which
migration may not be restricted by governments. We compare and contrast firstbest
efficiency (with migration controls) and federal efficiency (without migration controls).
We show that firstbest
efficiency requires maximising total product net of migration
cost, while federal efficiency does not. We also show that migration costs may lead to a
discontinuous federal utilitypossibility
frontier and to discontinuous regional reaction
functions. We establish that decentralised equilibrium allocations may not be firstbest
efficient but are federally efficient. We conclude by tying together wellunderstood
results from the limiting cases of free mobility and immobility with our results for the
intermediate case.*

#### Agent-based modelling of shifting cultivation field patterns, Vietnam

*Shifting cultivation in the Nghe An Province of Vietnam’s Northern Mountain
Region produces a characteristic land-cover pattern of small and larger fields.
The pattern is the result of farmers cultivating either individually or in spatially
clustered groups. Using spatially explicit agent-based modelling, and relying on
empirical data from fieldwork and observations for parameterization of
variables, the level of clustering in agricultural fields observed around a study
village is reproduced. Agents in the model act to maximize labour productivity,
which is based on potential yield and labour costs associated with fencing of
fields, and are faced with physical constraints. The simulation results are
compared with land-cover data obtained from remote sensing. Comparisons are
made on patterns as detected visually and using the mean nearest-neighbour
ratio. Baseline simulation outputs show high degrees of spatial clustering and
similarity to the land-cover data, but also a need for further calibration of model
variables and controls.*

#### Behavioral conformity in games with many players

M. Wooders and E. Cartwright and R. Selten, 2006

*In the literature of psychology and economics it is frequently observed that individuals tend to conform
in their behavior to that of similar individuals. A fundamental question is whether the outcome of such
conformity can be consistent with self-interest. We propose that this consistency requires the existence of a
Nash or approximate Nash equilibrium that induces a partition of the player set into relatively few societies,
each consisting of similar individuals playing similar strategies. In this paper we characterize a family of
games admitting the existence of such equilibrium. We also introduce the concept of ‘crowding types’ into
our description of players and distinguish between the crowding type of a player—those characteristics
of a player that have direct effects on others—and his tastes. With assumptions of ‘within crowding type
anonymity’ and ‘linearity of taste-types’ we show that the number of societies can be uniformly bounded.*

#### When is reputation bad?

J. Ely and D. Fudenberg and D. K. Levine, 2005

*In traditional reputation models, the ability to build a reputation is good for the long-run player. In [Ely, J.,
Valimaki, J., 2003. Bad reputation. NAJ Econ. 4, 2; http://www.najecon.org/v4.htm. Quart. J. Econ. 118
(2003) 785–814], Ely and Valimaki give an example in which reputation is unambiguously bad. This paper
characterizes a class of games in which that insight holds. The key to bad reputation is that participation
is optional for the short-run players, and that every action of the long-run player that makes the short-run
players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.”We
allow a broad set of commitment types, allowing many types, including the “Stackelberg type” used to prove
positive results on reputation. Although reputation need not be bad if the probability of the Stackelberg type
is too high, the relative probability of the Stackelberg type can be high when all commitment types are
unlikely.*

#### Equilibrium learning in simple contests

*The paper studies a repeated contest when contestants are uncertain about their true relative abilities.
When ability and effort are complements, a favorable belief about one’s own ability stimulates effort and
increases the likelihood of success. Success, in turn, reinforces favorable beliefs. We show that this implies
that with positive probability players fail to learn their true relative abilities in equilibrium, and one player
wins the contest with high probability forever. In this case, the prevailing player may be the actually worse
player, and persistent inequality arises. We discuss some features of the model when the complementarity
assumption is dropped.*

#### An initial implementation of the Turing tournament to learning in repeated two-person games

J. Arifovic and R. D. McKelvey and S. Pevnitskaya, 2006

*We report on a design of a Turing tournament and its initial implementation to learning in repeated 2-
person games. The principal objectives of the tournament, named after the original Turing Test, are (1) to
find learning algorithms (emulators) that most closely simulate human behavior, (2) to find algorithms (detectors)
that most accurately distinguish between humans and machines, and (3) to provide a demonstration
of how to implement this methodology for evaluating models of human behavior. In order to test our concept,
we developed the software and implemented a number of learning models well known in the literature
and developed a few detectors. This initial implementation found significant differences in data generated
by these learning models and humans, with the greatest ones in coordination games. Finally, we investigate
the stability of our result with respect to different evaluation approaches.*

#### Network topology and the efficiency of equilibrium

*Different kinds of networks, such as transportation, communication, computer, and supply networks, are
susceptible to similar kinds of inefficiencies. These arise when congestion externalities make the cost for
each user depend on the other users’ choice of routes. If each user chooses the least expensive (e.g., the
fastest) route from the users’ common point of origin to the common destination, the result may be Pareto
inefficient in that an alternative choice of routes would reduce the costs for all users. Braess’s paradox
represents an extreme kind of inefficiency, in which the equilibrium costs may be reduced by raising the
cost curves. As this paper shows, this paradox occurs in an (undirected) two-terminal network if and only
if it is not series-parallel. More generally, Pareto inefficient equilibria occur in a network if and only if one
of three simple networks is embedded in it.*

#### Coordination and cooperation in local, random and small world networks: Experimental evidence

*A laboratory experiment has been designed to study coordination and cooperation in games played on
local, random and small-world networks. For the coordination game, the results revealed a tendency for coordination
on the payoff-dominant equilibrium in all three networks, but the frequency of payoff-dominant
choices was significantly higher in small-world networks than in local and random networks. For the prisoner’s
dilemma game, cooperation was hard to reach on all three networks, with average cooperation lower in
small-world networks than in random and local networks. Two graph-theoretic characteristics—clustering
coefficient and characteristic path length—exhibited a significant effect on individual behavior, possibly
explaining why the small-world network, with its high clustering coefficient and short path length, is the
architecture of relations that drive a system towards equilibrium at the quickest pace.*

#### The evolution of cooperation through imitation

D. K. Levine and W. Pesendorfer

*We study evolutionarily stable outcomes for a class of games that admit cooperation and conflict as
possible Nash equilibria. We make use of two ideas: existing strategies are more likely to be imitated than
new strategies are to be introduced; players are able to identify opponents’ behavior prior to interaction.
The long-run evolutionary limit is efficient for the case of perfect recognition of opponents’ behavior. For
the case of imperfect recognition, efficiency is not achieved and long-run outcomes are more efficient the
more accurate is the information. Strategies that emerge in the long run are those where players reward
opponents who are likely to play the same way, and punish opponents who are likely to play differently.*

#### Bounded rationality in agent-based models: experiments with evolutionary programs

*This paper examines the use of evolutionary programming in agent-based
modelling to implement the theory of bounded rationality. Evolutionary
programming, which draws on Darwinian analogues of computing to create
software programs, is a readily accepted means for solving complex computational
problems. Evolutionary programming is also increasingly used to develop
problem-solving strategies in accordance with bounded rationality, which
addresses features of human decision-making such as cognitive limits, learning,
and innovation. There remain many unanswered methodological and conceptual
questions about the linkages between bounded rationality and evolutionary
programming. This paper reports on how changing parameters in one variant of
evolutionary programming, genetic programming, affects the representation of
bounded rationality in software agents. Of particular interest are: the ability of
agents to solve problems; limits to the complexity of agent strategies; the
computational resources with which agents create, maintain, or expand
strategies; and the extent to which agents balance exploration of new strategies
and exploitation of old strategies.*

#### Noncooperative Bargaining and Spatial Competition

H. Bester, 1989. Econometrica

*The paper presents a bargaining approach to spatial competition. Sellers compete by
choosing locations in a market region. Consumers face a cost to moving from one
place to another. The price od the good is determined as the perfect equilibrium
of a bargaining game between seller and buyer. In this game, the consumer has the
outside option to move to another seller so that prices at all stores are
independent. Existence od a location-price equilibrium is established. The
outcome approaches the perfectly competitive one if the consumer's costs of
traveling become negligible or if the number of sellers tends to infinity.*

#### The Evolution of Cooperation in Heterogeneous Populations

S. Bowles and H. Gintis, 2003

*How do human groups maintain a high level of cooperation despite a low
level of genetic relatedness among group members? We suggest that many
humans have a predisposition to punish those who violate group-beneficial
norms, even when this reduces their fitness relative to other group members.
Such altruistic punishment is widely observed to sustain high levels of cooperation
in behavioral experiments and in natural settings. It is known that if
group extinctions are sufficiently common, altruistic punishment may evolve
through the contribution of norm adherence to group survival. Additionally,
those engaging in punishment of norm violators may reap fitness benefits if
their punishment is treated as a costly signal of some underlying but unobservable
quality as a mate, coalition partner, or opponent. Here we explore a
different mechanism in which neither signaling nor group extinctions plays a
role. Rather, punishment takes the form of ostracism or shunning, and those
punished in this manner suffer fitness costs.
We offer a model of this behavior, which we call strong reciprocity: where
members of a group benefit from mutual adherence to a social norm, strong
reciprocators obey the norm and punish its violators, even though they receive
lower payoffs than other group members, such as selfish agents who violate
the norm and do not punish, and pure cooperators who adhere to the norm
but free-ride by never punishing. Our agent-based simulations show that,
under assumptions approximating some likely human environments over the
100,000 years prior to the domestication of animals and plants, the proliferation
of strong reciprocators when initially rare is highly likely, and that
substantial frequencies of all three behavioral types can be sustained in a
population.*

#### Generous and Greedy Strategies

B. Carlsson and S. Johansson, 1998

*We introduce generous, ecent-matched, and greedy strategies as concepts for
analyzing games. A two person prisioner's dilemma game is described by the
four outcomes (C,D), (C,C), (D,C) and (D,D). In a generous strategy the
proportion of (C,D) is larger than (D,C), i.e. the probability of facing
defect is larger than the probability of defecting, An event-matched strategy
has the (C,D) proportion approximately equal to that of (D,C). A greedy
strategy is an inverted generous atrategy. The basis of the partition is that
it is a zero-sum game given that the sum of the proportions of strategies (C,D)
must equal that of (D,C). In a population simulation, we compare the PD game
with the chicken game (CG), given complete as well as partial knowledge of the
rules for moves in the other strategies. In a traffic intersection example, we
expected a co-operating generous strategy to be successful when the cost for
mutual collision was high in addition to the presence of uncertainty. The
simulation indeed showed that a generous strategy was successful in the CG part,
in which agents faced uncertainty about the outcome. If the resulting zero-sum
game is changed from a PD game to a CG, of if the noise level is increased, the
sucessful strategies will favor a generous strategy rather an even-matched or
greedy strategy.*

#### Spatial and Density Effects in Evolutionary Game Theory

R. Cressman and G. T. Vickers, 1996

*Two models are considered for the study of game dynamics in a spatial domain.
Both models are continuous in space and time and give rise to reaction-diffusion
equations. The spatial domain is homogeneous but the mobility of the individuals
is allowed to depend upon the strategy. The models are analysed for spatial
patterns (via a Turing instability) and also for the direction of the travelling
wave that replaces one strategy by another. It is shown that the qualitative
behaviour of the two models is quite different. When considering the existence
of spatial patterns and deciding whether increased mobility is helpful or not,
it is shown that the answers depend crucially upon the model equations. Since
both models (in the absence of spatial variation) are quite standard, it is clear
that considerable care has to be exercised in the formulation of spatial models
and in their interpretation.*

#### Modern Game Theory: Deduction vs. Induction

The aim of this paper is twofold: firstly, to present a survey of the theory of games, and secondly, to contrast deductive and inductive reasoning in game theory. This report begins with an overview of the classical theory of strategic form games of complete information. This theory is based on the traditional economic assumption of rationality, common knowledge of which yields Nash equilibrium as a deductive solution to games in this class. In the second half of this paper, modern game-theoretic ideas are introduced. In particular, learning and repeated games are analyzed using an inductive model, in the absence of common knowledge. In general, inductive reasoning does not gives rise to the Nash equilibrium when learning is deterministic, unless initial beliefs are somehow fortuitously chosen. However, computer simulations show that in the presence of a small random component, repeated play does indeed converge to Nash equilibrium. This research is of interest to computer scientists because modern game theory is a natural framework in which to formally study multi-agent systems and distributed computing.

#### Self-organized Criticality in Spatial Evolutionary Game Theory

T. Killingback and M. Doebeli, 1997

*Self-organized criticality is an important framework for understanding the
emergence of scale-free natural phenomena. Cellular automata provide simple
interesting models in which to study self-organized criticality. We consider the
dynamics of a new class of cellular automata which are constructed as natural
spatial extensions of evolutionary game theory. This construction yields a
discrete one-parameter family of cellular automata. We show that there is a range
of parameter values for which this system exhibits complex dynamics with long
range correlations between states in both time and space. In this region the
dynamics evolve to a self-organized critical state in which structures exist on
all time and length scales, and the relevant statistical measures have power
law behaviour.*

#### Concentration of Competing Retail Stores

*The geographical concentration of stores that sell similar commodities is
analyzed using a two-dimensional spatial competition model. A higher
concentration of stores attracts more consumers with taste uncertainty and low
price expectations (a market-size effect), while it leads to fiercer price
competition (a price-cutting effect). Our model is general enough to allow
for the coexistence of multiple (possibly) asymmetric clusters of stores. We
provide sufficient conditions for the nonemptiness of equilibrium store location
choices in pure strategies. Through numerical examples, we illustrate the
trade-off between the market-size and price-cutting effects, and provide
agglomeration patterns of stores in special cases.*

#### Discrete Time Spatial Models Arising in Genetics, Evolutionary Game Theory, and Branching Processes

J. Radcliffe and L. Rass, 1996

*A saddle point method is used to obtain the speed of first spread of new
genotypes in genetic models and of new strategies in game theoretic models. It is
also used to obtain the speed of the forward tail of the distribution of farthest
spread for branching process models. The technique is applicable to a wide range
of models. They include multiple allele and sex-linked models in genetics,
multistrategy and bimatrix evolutionary games, and multitype and demographic
branching processes. The speed of propagation has been obtained for genetics
models (in simple cases only) by Weinberger [1, 2] and Lui [3-7], using exact
analytical methods. The exact results were obtained only for two-allele,
single-locus genetic models. The saddle point method agrees in these very
simple cases with the results obtained by using the exact analytic methods.
Of course, it can also be used in much more general situations far less tractable
to exact analysis. The connection between genetic and game theoretic models is
also briefly considered, as is the extent to which the exact analytic methods
yield results for simple models in game theory.*

#### Nash equilibrium in a spatial model of coalition bargaining

*In the model presented here, n parties choose policy positions in a space Z
of dimension at least two. Each party is represented by a "principal" whose true
policy preferences on Z are unknown to other principals. In the first version of
the model the party declarations determine the lottery outcome of coalition
negotiation. The coalition risk functions are common knowledge to the parties.
We assume these coalition probabilities are inversely proportional to the
variance of the declarations of the parties in each coalition. It is shown that
with this outcome function and with three parties there exists a stable, pure
strategy Nash equilibrium, z* for certain classes of policy preferences. This
Nash equilibrium represents the choice by each party principal of the position
of the party leader and thus the policy platform to declare to the electorate.
The equilibrium can be explicitly calculated in terms of the preferences of the
parties and the scheme of private benefits from coalition membership. In
particular, convergence in equilibrium party positions is shown to occur if the
principals' preferred policy points are close to colinear. Conversely, divergence
in equilibrium party positions occurs if the bliss points are close to
symmetric. If private benefits (the non-policy perquisites from coalition
membership) are sufficiently large (that is, of the order of policy benefits),
then the variance in equilibrium party positions is less than the variance in
ideal points. The general model attempts to incorporate party beliefs concerning
electoral responses to party declarations. Because of the continuity properties
imposed on both the coalition and electoral risk functions, there will exist
mixed strategy Nash equilibria. We suggest that the existence of stable, pure
strategy Nash equilibria in general political games of this type accounts for the
non-convergence of party platforms in multiparty electoral systems based on
proportional representation.*

#### Stability of Spatial Equilibrium

*We consider interregional migration, where regions may be interpreted as clubs,
social subgroups, or strategies. Using the positive definite adaptive (PDA)
dynamics, which include the replicator dynamics, we examine the evolutionary
stable state (ESS) and the asymptotic stability of the spatial distribution of
economic activities in a multiregional system. We derive an exact condition
for the equivalence between ESS and asymptotically stable equilibrium in each
PDS dynamic. We show that market outcome yields the efficiency allocation of
population with an additional condition. We also show that interior equilibria
are stable in the presence of strong congestion diseconomies but unstable in the
presence of strong agglomeration economies with further condition.*

#### Spatial Games with Adaptive Tit-for-Tats

*This paper presents an adaptive tit-for-tat strategy and a study of its
behavior in spatial IPD games. The adaptive tit-for-tat strategy is shown
elsewhere to demonstrate high performance in IPD tournaments or individual
IPD games with other types of strategies, and obtains higher scores than the
pure tit-for-tat strategy. In spatial IPD games, the strategy exhibits stability and
resistance to perturbations, and those properties are more pronounced in
variations of the spatial game model that induce some degree of “noise” :
probabilistic winning, spatial irregularity and continuous time. The adaptive tit-
for-tat strategy is also compared to pure tit-for-tat and found to be more stable
and predominant in perturbed environments.*

### Journals

Games and Economic Behaviour

IJGIS special issue on spatial agent-based modelling 2006

### Books

Riccardo Boero - The Spatial Dimension and Social Simulations: A Review of Three Books. Um texto interessante e uma boa revisao de tres livros tratando de sistemas de agentes e da importancia da dimensao espacial. The Spatial Dimension and Social Simulations

Caípitulo 2 do Russel sobre agentes.

### Pages

Program for Evolutionary Dynamics (Harvard University)

### Authors

#### Samuel Bowles

with **Suresh Naidu**: Institutional Equilibrium Selection by Intentional Idiosyncratic Play, 2004

with **Hebert Gintis**: The inheritance of inequality, 2002

#### Portugali e Benenson

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