How noise matters. (English) Zbl 1056.91011
Summary: Recent advances in evolutionary game theory have introduced noise into decisionmaking to select in favor of certain equilibria in coordination games. Noisy decisionmaking is justified on bounded rationality grounds, and consequently the sources of noise are left unmodelled. This methodological approach can only be successful if the results do not depend too much on the nature of the noise process. This paper investigates invariance to noise of these results, both for the random matching paradigm that has characterized much of the recent literature and for a larger class of two-strategy population games where payoffs may vary non-linearly with the distribution of strategies among the population. Several parametrizations of noise reduction are investigated. The results show that a symmetry property of the noise process and, in the case of non-linear payoffs, bounds on the asymmetry of the payoff functions suffice to preserve the known stochastic stability results.
References:
| [1] | Bergin, J.; Lipman, B., Evolution with state-dependent mutations, Econometrica, 64, 943-956 (1996) · Zbl 0862.90142 |
| [2] | Blume, L. E., The statistical mechanics of strategic interaction, Games Econ. Behav., 4, 387-424 (1993) · Zbl 0797.90123 |
| [3] | Blume, L. E., An Evolutionary Analysis of Keynsian Coordination Failure (1994), Cornell University |
| [4] | Blume, L. E., Evolutionary Equilibrium with Forward-Looking Players (1995), Cornell University |
| [5] | Blume, L. E., Population Games, (Arthur, W. B.; Lane, D.; Durlauf, S., The Economy as an Complex Adaptive System II (1997), Addison-Wesley: Addison-Wesley Redwood City) |
| [6] | Blume, L.E., Durlauf, S., 1997. Equilibrium concepts for social interaction models, Int. Game Theory Rev. Forthcoming; Blume, L.E., Durlauf, S., 1997. Equilibrium concepts for social interaction models, Int. Game Theory Rev. Forthcoming · Zbl 1086.91018 |
| [7] | Brock, W.; Durlauf, S., Interactions based models, (Heckman, J.; Leamer, E., Handbook of Econometrics (2000), North-Holland: North-Holland Amsterdam) |
| [8] | Brock, W.; Durlauf, S., Discrete choice with social interactions, Rev. Econ. Stud., 59, 235-260 (2001) · Zbl 0980.91016 |
| [9] | Canning, D., Average behavior in learning models, J. Econ. Theory, 57, 442-472 (1992) · Zbl 0760.90101 |
| [10] | Durrett, R., Probability: Theory and Examples (1991), Wadsworth & Brooks: Wadsworth & Brooks Pacific Grove, CA · Zbl 0709.60002 |
| [11] | Foster, D.; Young, H. P., Stochastic evolutionary game dynamics, Theoret. Population Biol., 38, 219-232 (1990) · Zbl 0703.92015 |
| [12] | Fudenberg, D.; Harris, C., Evolutionary dynamics with aggregate shocks, J. Econ. Theory, 57, 2, 420-441 (1992) · Zbl 0766.92012 |
| [13] | Kandori, M.; Mailath, G.; Rob, R., Learning, mutation and long run equilibrium in games, Econometrica, 61, 29-56 (1993) · Zbl 0776.90095 |
| [14] | Karlin, S., A First Course in Stochastic Processes (1966), Academic Press: Academic Press New York · Zbl 0177.21102 |
| [15] | Kingman, J. F.C., Poisson Processes (1993), Oxford Univ. Press: Oxford Univ. Press New York · Zbl 0771.60001 |
| [16] | Monderer, D.; Shapley, L., Potential games, Games Econ. Behav., 1, 124-143 (1996) · Zbl 0862.90137 |
| [17] | Rosenthal, R., A class of games possessing pure strategy Nash equilibria, Int. J. Game Theory, 2, 65-67 (1973) · Zbl 0259.90059 |
| [18] | Samuelson, L., Stochastic stability in games with alternative best replies, J. Econ. Theory, 64, 35-65 (1994) · Zbl 0811.90138 |
| [19] | Young, H. P., The evolution of conventions, Econometrica, 61, 57-84 (1993) · Zbl 0773.90101 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
