14,113 research outputs found
On the expected number of equilibria in a multi-player multi-strategy evolutionary game
In this paper, we analyze the mean number of internal equilibria in
a general -player -strategy evolutionary game where the agents' payoffs
are normally distributed. First, we give a computationally implementable
formula for the general case. Next we characterize the asymptotic behavior of
, estimating its lower and upper bounds as increases. Two important
consequences are obtained from this analysis. On the one hand, we show that in
both cases the probability of seeing the maximal possible number of equilibria
tends to zero when or respectively goes to infinity. On the other hand,
we demonstrate that the expected number of stable equilibria is bounded within
a certain interval. Finally, for larger and , numerical results are
provided and discussed.Comment: 26 pages, 1 figure, 1 table. revised versio
Stochastically Stable Equilibria in Coordination Games with Multiple Populations
We investigate the equilibrium selection problem in n-person binary coordination games by means of adaptive play with mistakes (Young 1993). The size and the depth of a particular type of basins of attraction are found to be the main factors in determining the selection outcome. The main result shows that if a strategy has the larger basin of attraction, and if it is deep enough, then the strategy constitutes a stochastically stable equilibrium. The existence of games with multiple stochastically stable equilibria is an immediate consequence of the result. We explicitly address the qualitative difference between selection results in multi-dimensional stochastic evolution models and those in single dimensional models, and shed some light on the source of the difference.Equilibrium selection, stochastic stability, unanimity game, coordination game
Punishment in Public Goods games leads to meta-stable phase transitions and hysteresis
The evolution of cooperation has been a perennial problem in evolutionary
biology because cooperation can be undermined by selfish cheaters who gain an
advantage in the short run, while compromising the long-term viability of the
population. Evolutionary game theory has shown that under certain conditions,
cooperation nonetheless evolves stably, for example if players have the
opportunity to punish cheaters that benefit from a public good yet refuse to
pay into the common pool. However, punishment has remained enigmatic because it
is costly, and difficult to maintain. On the other hand, cooperation emerges
naturally in the Public Goods game if the synergy of the public good (the
factor multiplying the public good investment) is sufficiently high. In terms
of this synergy parameter, the transition from defection to cooperation can be
viewed as a phase transition with the synergy as the critical parameter. We
show here that punishment reduces the critical value at which cooperation
occurs, but also creates the possibility of meta-stable phase transitions,
where populations can "tunnel" into the cooperating phase below the critical
value. At the same time, cooperating populations are unstable even above the
critical value, because a group of defectors that are large enough can
"nucleate" such a transition. We study the mean-field theoretical predictions
via agent-based simulations of finite populations using an evolutionary
approach where the decisions to cooperate or to punish are encoded genetically
in terms of evolvable probabilities. We recover the theoretical predictions and
demonstrate that the population shows hysteresis, as expected in systems that
exhibit super-heating and super-cooling. We conclude that punishment can
stabilize populations of cooperators below the critical point, but it is a
two-edged sword: it can also stabilize defectors above the critical point.Comment: 22 pages, 9 figures. Slight title change, version that appears in
Physical Biolog
The Evolutionary Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game
The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents\u27 rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve.
Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents.
Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature
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