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3013. Stability in games with random payoffs

Invited abstract in session WB-35: Stochastic optimization: theory and applications, stream Stochastic, Robust and Distributionally Robust Optimization.

Wednesday, 10:30-12:00
Room: 44 (building: 303A)

Authors (first author is the speaker)

1. Lukáš Račko
Department of probability and mathematical statistics, Faculty of mathematics and physics, Charles university
2. Milos Kopa
Department of Probability and Mathematical Statistics, Charles University in Prague, Faculty of Mathematics and Physics
3. Petr Lachout
Dept. Probability and Statistics, Charles University in Praha

Abstract

The paper deals with non-cooperative games in which the payoff function of its players is influenced by exogenous randomness. The main goal is to provide a general concept of stability in those games because the standard notion of Nash equilibrium is no longer satisfactory. One could find a deterministic equivalent to the game with a random payoff by considering a risk measure and defining a new game with a payoff function adjusted by the risk measure. This, however, causes several problems as the Fundamental Theorem of non-cooperative game theory no longer holds for most of such defined equivalents. Our idea is to loosen the standard concept of the best response to an alpha-best response which requires the strategy to be the best response only with a certain high probability. Based on this idea we define the alpha-Nash equilibria and we prove that for every finite game with random payoff non-trivial alpha-Nash equilibria exist. Moreover, those equilibria characterize equilibria in a broad class of deterministic equivalent games. Finally, we extend the idea of a static game with a random payoff to a game with multiple stages and we show that every finite stochastic game may be represented as a sequential game with a random payoff. In the numerical study, this theory is applied to a management problem of competition of hospitals for vaccines during a pandemic.

Keywords

Status: accepted

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