TY - GEN

T1 - Oblivious equilibrium for stochastic games with concave utility

AU - Adlakha, Sachin

AU - Johari, Ramesh

AU - Weintraub, Gabriel

AU - Goldsmith, Andrea

PY - 2008

Y1 - 2008

N2 - We study stochastic games with a large number of players, where players are coupled via their payoff functions. A standard solution concept for stochastic games is Markov perfect equilibrium (MPE). In MPE, each player's strategy is a function of its own state as well as the state of other players. This makes MPE computationally prohibitive as the number of players becomes large. An approximate solution concept called oblivious equilibrium (OE) was introduced by Weintraub et al., where each player's decision depends only on its own state and the "long-run average" state of other players. This makes OE computationally more tractable than MPE. It was shown that under a set of assumptions, as the number of players becomes large, OE closely approximates MPE. However, these assumptions require the computation of OE and verifying that the resulting stationary distribution satisfies a certain light-tail condition. In this paper, we derive exogenous conditions on the state dynamics and the payoff function under which the light-tail condition holds. A key condition is that the agents' payoffs are concave in their own state and actions. These exogenous conditions enable us to characterize a family of stochastic games in which OE is a good approximation for MPE.

AB - We study stochastic games with a large number of players, where players are coupled via their payoff functions. A standard solution concept for stochastic games is Markov perfect equilibrium (MPE). In MPE, each player's strategy is a function of its own state as well as the state of other players. This makes MPE computationally prohibitive as the number of players becomes large. An approximate solution concept called oblivious equilibrium (OE) was introduced by Weintraub et al., where each player's decision depends only on its own state and the "long-run average" state of other players. This makes OE computationally more tractable than MPE. It was shown that under a set of assumptions, as the number of players becomes large, OE closely approximates MPE. However, these assumptions require the computation of OE and verifying that the resulting stationary distribution satisfies a certain light-tail condition. In this paper, we derive exogenous conditions on the state dynamics and the payoff function under which the light-tail condition holds. A key condition is that the agents' payoffs are concave in their own state and actions. These exogenous conditions enable us to characterize a family of stochastic games in which OE is a good approximation for MPE.

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U2 - 10.1109/ALLERTON.2008.4797711

DO - 10.1109/ALLERTON.2008.4797711

M3 - Conference contribution

AN - SCOPUS:64549138972

SN - 9781424429264

T3 - 46th Annual Allerton Conference on Communication, Control, and Computing

SP - 1304

EP - 1308

BT - 46th Annual Allerton Conference on Communication, Control, and Computing

T2 - 46th Annual Allerton Conference on Communication, Control, and Computing

Y2 - 24 September 2008 through 26 September 2008

ER -