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On the Equivalence of Nash and Evolutionary Equilibrium in Finite Populations, CeDEx Discussion Paper No
, 2008
"... This paper provides su ¢ cient and partially necessary conditions for the equivalence of symmetric Nash and evolutionary equilibrium in symmetric games played by …nite populations. The conditions are based on generalized constantsum and ”smallness ” properties, the latter of which is known from mod ..."
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This paper provides su ¢ cient and partially necessary conditions for the equivalence of symmetric Nash and evolutionary equilibrium in symmetric games played by …nite populations. The conditions are based on generalized constantsum and ”smallness ” properties, the latter of which is known from models of perfect competition and large games. The conditions are illustrated on examples including oligopoly games.
Globally evolutionarily stable portfolio rules,
 Journal of Economic Theory,
, 2008
"... Abstract The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixedmix investment strategies (portfolio rules), dist ..."
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Cited by 2 (1 self)
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Abstract The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixedmix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to "survive," i.e. to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this propertyan analogue of the famous Kelly (1956) rule of "betting one's beliefs." A game theoretic interpretation of this result is given. JELClassification: G11, C61, C62.
The Reality Game ∗
, 902
"... We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the ‘rea ..."
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We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the ‘reality map’, which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers to a purely subjective game in which probabilities equal the amount wagered. We study selfreinforcing games, in which betting more on an outcome increases its odds, and selfdefeating games, in which the opposite is true. This is investigated in and out of equilibrium, with and without rational players, and both numerically and analytically. We introduce a method of measuring the inefficiency of the game, similar to measuring the magnitude of the arbitrage opportunities in a financial market. We prove that convergence to equilibrium is is a power law with an extremely slow rate of convergence: The more subjective the game, the slower the convergence.