175 research outputs found
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 figure
The Evolution of Fairness under an Assortative Matching Rule in the Ultimatum Game
This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.
Coevolution of trustful buyers and cooperative sellers in the trust game
Many online marketplaces enjoy great success. Buyers and sellers in
successful markets carry out cooperative transactions even if they do not know
each other in advance and a moral hazard exists. An indispensable component
that enables cooperation in such social dilemma situations is the reputation
system. Under the reputation system, a buyer can avoid transacting with a
seller with a bad reputation. A transaction in online marketplaces is better
modeled by the trust game than other social dilemma games, including the
donation game and the prisoner's dilemma. In addition, most individuals
participate mostly as buyers or sellers; each individual does not play the two
roles with equal probability. Although the reputation mechanism is known to be
able to remove the moral hazard in games with asymmetric roles, competition
between different strategies and population dynamics of such a game are not
sufficiently understood. On the other hand, existing models of reputation-based
cooperation, also known as indirect reciprocity, are based on the symmetric
donation game. We analyze the trust game with two fixed roles, where trustees
(i.e., sellers) but not investors (i.e., buyers) possess reputation scores. We
study the equilibria and the replicator dynamics of the game. We show that the
reputation mechanism enables cooperation between unacquainted buyers and
sellers under fairly generous conditions, even when such a cooperative
equilibrium coexists with an asocial equilibrium in which buyers do not buy and
sellers cheat. In addition, we show that not many buyers may care about the
seller's reputation under cooperative equilibrium. Buyers' trusting behavior
and sellers' reputation-driven cooperative behavior coevolve to alleviate the
social dilemma.Comment: 5 figure
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game
Aspiration-based evolutionary dynamics have recently been used to model the evolution of fair play in the ultimatum game showing that incredible threats to reject low offers persist in equilibrium. We focus on two extensions of this analysis: we experimentally test whether assumptions about agent motivations (aspiration levels) and the structure of the game (binary strategy space) reflect actual play, and we examine the problematic assumption embedded in the standard replicator dynamic that unhappy agents who switch strategies may return to a rejected strategy without exploring other options. We find that the resulting "no switchback" dynamic predicts the evolution of play better than the standard dynamic and that aspirations are a significant motivator for our participants. In the process, we also construct and analyze a variant of the ultimatum game in which players can adopt conditional (on their induced aspirations) stategies.ultimatum game, learning, aspirations, replicator dynamics, experiment
The evolution of social norms
Evolutionary game theory provides the tools to analyze which strategies, or patterns of behaviour, emerge over time through a process of adaptation. Social norms can be defined as patterns of behaviour with certain characteristics. Evolutionary game theory thus provides one perspective on how social norms are formed and maintained. Prisoner's dilemma games can be used to study the conditions under which cooperative norms emerge. Bargaining games can be used to address the formation of fairness norms. However, being more congenial to analyzing norms that somehow focus on material payoffs, it is not a given that evolutionary game theory can adequately address norms focusing on rights or virtues.Evolutionary game theory Social norms
- …