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 -