29,380 research outputs found
On imitation dynamics in potential population games
Imitation dynamics for population games are studied and their asymptotic
properties analyzed. In the considered class of imitation dynamics - that
encompass the replicator equation as well as other models previously considered
in evolutionary biology - players have no global information about the game
structure, and all they know is their own current utility and the one of fellow
players contacted through pairwise interactions. For potential population
games, global asymptotic stability of the set of Nash equilibria of the
sub-game restricted to the support of the initial population configuration is
proved. These results strengthen (from local to global asymptotic stability)
existing ones and generalize them to a broader class of dynamics. The developed
techniques highlight a certain structure of the problem and suggest possible
generalizations from the fully mixed population case to imitation dynamics
whereby agents interact on complex communication networks.Comment: 7 pages, 3 figures. Accepted at CDC 201
On stochastic imitation dynamics in large-scale networks
We consider a broad class of stochastic imitation dynamics over networks,
encompassing several well known learning models such as the replicator
dynamics. In the considered models, players have no global information about
the game structure: they only know their own current utility and the one of
neighbor players contacted through pairwise interactions in a network. In
response to this information, players update their state according to some
stochastic rules. For potential population games and complete interaction
networks, we prove convergence and long-lasting permanence close to the
evolutionary stable strategies of the game. These results refine and extend the
ones known for deterministic imitation dynamics as they account for new
emerging behaviors including meta-stability of the equilibria. Finally, we
discuss extensions of our results beyond the fully mixed case, studying
imitation dynamics where agents interact on complex communication networks.Comment: Extended version of conference paper accepted at ECC 201
Imitation Dynamics in Population Games on Community Networks
We study the asymptotic behavior of deterministic, continuous-time imitation
dynamics for population games over networks. The basic assumption of this
learning mechanism -- encompassing the replicator dynamics -- is that players
belonging to a single population exchange information through pairwise
interactions, whereby they get aware of the actions played by the other players
and the corresponding rewards. Using this information, they can revise their
current action, imitating the one of the players they interact with. The
pattern of interactions regulating the learning process is determined by a
community structure. First, the set of equilibrium points of such network
imitation dynamics is characterized. Second, for the class of potential games
and for undirected and connected community networks, global asymptotic
convergence is proved. In particular, our results guarantee convergence to a
Nash equilibrium from every fully supported initial population state in the
special case when the Nash equilibria are isolated and fully supported.
Examples and numerical simulations are offered to validate the theoretical
results and counterexamples are discussed for scenarios when the assumptions on
the community structure are not verified.Comment: 12 pages, 5 figures. Under revie
On stochastic imitation dynamics in large-scale networks
We consider a broad class of stochastic imitation dynamics over networks,
encompassing several well known learning models such as the replicator
dynamics. In the considered models, players have no global information about
the game structure: they only know their own current utility and the one of
neighbor players contacted through pairwise interactions in a network. In
response to this information, players update their state according to some
stochastic rules. For potential population games and complete interaction
networks, we prove convergence and long-lasting permanence close to the
evolutionary stable strategies of the game. These results refine and extend the
ones known for deterministic imitation dynamics as they account for new
emerging behaviors including meta-stability of the equilibria. Finally, we
discuss extensions of our results beyond the fully mixed case, studying
imitation dynamics where agents interact on complex communication networks.Comment: Extended version of conference paper accepted at ECC 201
Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition
Schaffer (1988) proposed a concept of evolutionary stability for finite-population models that has interesting implications in economic models of evolutionary learning, since it is related to perfectly competitive equilibrium. The present paper explores the relation of this concept to Nash equilibrium in particular classes of games, including constant-sum games, games with weak payoff externalities, and games where imitative decision rules are individually improving. An illustration of the latter is provided in the context of Bertrand oligopoly with homogeneous product which allows for a characterization of the set of evolutionarily stable prices.
Imitators and Optimizers in Cournot Oligopoly
We analyze a symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a l`a Vega-Redondo (1997). Optimizers play a myopic best response to the opponentsā previous output. Firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953)
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