7,663 research outputs found
Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback
We study the evolutionary dynamics of games under environmental feedback
using replicator equations for two interacting populations. One key feature is
to consider jointly the co-evolution of the dynamic payoff matrices and the
state of the environment: the payoff matrix varies with the changing
environment and at the same time, the state of the environment is affected
indirectly by the changing payoff matrix through the evolving population
profiles. For such co-evolutionary dynamics, we investigate whether convergence
will take place, and if so, how. In particular, we identify the scenarios where
oscillation offers the best predictions of long-run behavior by using
reversible system theory. The obtained results are useful to describe the
evolution of multi-community societies in which individuals' payoffs and
societal feedback interact.Comment: 7 pages, submitted to a conferenc
The Evolution of Social Norms and Individual Preferences
Why does an altruistically inclined player behave altruistically in some contexts and egoistically or spitefully in others? This article provides an economic explanation to this question. The basic argument is centered on the idea that social norms shape our preferences through a process of cultural learning. In particular, we claim that, in contexts with a stable norm of reciprocity, an altruistic player can respond in kind to egoistic or spiteful players by behaving either egoistically or spitefully when confronting them and yet continue to be an altruistic player. This is why, instead of studying the evolution of preferences as such, in this work we analyze the evolution of social norms that indirectly determine individual preferences and behavior. Such a study requires that we distinguish between players' behavioral preferences, or those individuals show with their behavior, and players' intrinsic preferences, or those they inherently support or favor. We argue that, whereas the former can change through the evolution of social norms, in this case a reciprocity norm, the latter are not subject to evolutionary pressures and, therefore, we assume them to be given.Social norms, reciprocity, endogenous preferences, asymmetric evolutionary game
The Shared Reward Dilemma
One of the most direct human mechanisms of promoting cooperation is rewarding
it. We study the effect of sharing a reward among cooperators in the most
stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically,
for a group of players that collect payoffs by playing a pairwise Prisoner's
Dilemma game with their partners, we consider an external entity that
distributes a fixed reward equally among all cooperators. Thus, individuals
confront a new dilemma: on the one hand, they may be inclined to choose the
shared reward despite the possibility of being exploited by defectors; on the
other hand, if too many players do that, cooperators will obtain a poor reward
and defectors will outperform them. By appropriately tuning the amount to be
shared a vast variety of scenarios arises, including traditional ones in the
study of cooperation as well as more complex situations where unexpected
behavior can occur. We provide a complete classification of the equilibria of
the -player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Finite-size fluctuations in coevolutionary dynamics arise in models of
biological as well as of social and economic systems. This brief tutorial
review surveys a systematic approach starting from a stochastic process
discrete both in time and state. The limit of an infinite
population can be considered explicitly, generally leading to a replicator-type
equation in zero order, and to a Fokker-Planck-type equation in first order in
. Consequences and relations to some previous approaches are
outlined.Comment: Banach Center publications, in pres
Open-ended Learning in Symmetric Zero-sum Games
Zero-sum games such as chess and poker are, abstractly, functions that
evaluate pairs of agents, for example labeling them `winner' and `loser'. If
the game is approximately transitive, then self-play generates sequences of
agents of increasing strength. However, nontransitive games, such as
rock-paper-scissors, can exhibit strategic cycles, and there is no longer a
clear objective -- we want agents to increase in strength, but against whom is
unclear. In this paper, we introduce a geometric framework for formulating
agent objectives in zero-sum games, in order to construct adaptive sequences of
objectives that yield open-ended learning. The framework allows us to reason
about population performance in nontransitive games, and enables the
development of a new algorithm (rectified Nash response, PSRO_rN) that uses
game-theoretic niching to construct diverse populations of effective agents,
producing a stronger set of agents than existing algorithms. We apply PSRO_rN
to two highly nontransitive resource allocation games and find that PSRO_rN
consistently outperforms the existing alternatives.Comment: ICML 2019, final versio
Evolutionary consequences of behavioral diversity
Iterated games provide a framework to describe social interactions among
groups of individuals. Recent work stimulated by the discovery of
"zero-determinant" strategies has rapidly expanded our ability to analyze such
interactions. This body of work has primarily focused on games in which players
face a simple binary choice, to "cooperate" or "defect". Real individuals,
however, often exhibit behavioral diversity, varying their input to a social
interaction both qualitatively and quantitatively. Here we explore how access
to a greater diversity of behavioral choices impacts the evolution of social
dynamics in finite populations. We show that, in public goods games, some
two-choice strategies can nonetheless resist invasion by all possible
multi-choice invaders, even while engaging in relatively little punishment. We
also show that access to greater behavioral choice results in more "rugged "
fitness landscapes, with populations able to stabilize cooperation at multiple
levels of investment, such that choice facilitates cooperation when returns on
investments are low, but hinders cooperation when returns on investments are
high. Finally, we analyze iterated rock-paper-scissors games, whose
non-transitive payoff structure means unilateral control is difficult and
zero-determinant strategies do not exist in general. Despite this, we find that
a large portion of multi-choice strategies can invade and resist invasion by
strategies that lack behavioral diversity -- so that even well-mixed
populations will tend to evolve behavioral diversity.Comment: 26 pages, 4 figure
On Evolutionary Stability of Spiteful Preferences
The paper analyzes under what conditions spiteful preferences are evolutionarily stable applying the indirect evolution approach. With a quadratic material payo¤ function, spiteful preferences are evolutionarily stable for a large set of parameters. It is shown that strategic substitutability or complementarity is endogenous property of the game played with evolutionarily stable preferences. Its relation to properties of the material payoff function is analyzed. Finally, it is shown that with incomplete information only selfish preferences are evolutionarily stable.indirect evolution;spite;endogenous preferences
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