Strategy (game theory) | EPFL Graph Search

In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends not only on their own actions but on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game. In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines. The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the

Multi-Agent Learning for Resource Allocation Problems

Ludek Cigler

We analyze resource allocation problems where N independent agents want to access C resources. Each resource can be only accessed by one agent at a time. In order to use the resources efficiently, the agents need to coordinate their access. We focus on decentralized coordination, i.e. coordination without central authority. We analyze coordination mechanisms for two different kind of agents: 1) cooperative, who follow the prescribed protocol entirely; and 2) non-cooperative, who attempt to maximize their own utility. We propose a novel approach to achieve a fair and efficient resource allocation when the agents are cooperative. The agents access resources in slots. At the beginning of each slot, they observe a global coordination signal – a random integer 1 ≤ k ≤ K . The agents then learn a different allocation for each value of the coordination signal. When modeled as a game, the canonical solution to the resource allocation problem is the correlated equilibrium. In a correlated equilibrium, a “smart” coordination device chooses the actions for the “stupid” agents, who then have no incentive to deviate from these recommendations. In contrast, in our solution the coordination signal is “stupid”, since it is not specific to the game. The agents are “smart”, because they learn their strategy independently for each signal value. We show that our learning algorithm converges to an efficient resource allocation in polynomial time. The resulting allocation becomes more fair as the number of signals K increases. A non-cooperative, self-interested agent can exploit our cooperative allocation scheme by accessing one resource all the time, until everyone else gives up. Therefore, for the non-cooperative agents, we consider an infinitely repeated resource allocation game with discounting. This game is symmetric and all the agents are identical, so we look for its symmetric subgame-perfect equilibria. (Bhaskar (2000)) proposed a solution for 2-agent, 1-resource allocation games: Agents start by symmetrically choosing their actions randomly, and as soon as they each choose different actions, they start to follow a convention that prescribes their actions from then on. We extend the concept of convention to the general resource allocation problems of N agents and C resources. We show that for any convention, there exists a symmetric subgame-perfect equilibrium that implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal that allows them to alternate between different allocations. We define the price of anonymity of a convention as the ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the convention. We show that the price of anonymity of the bourgeois convention is infinite. The market convention decreases this price by reducing the conflict between the agents.

EPFL2013

Symmetric subgame perfect equilibria in resource allocation

Ludek Cigler, Boi Faltings

We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N-agent, C-resource allocation problems. (Bhaskar 2000) proposed one way to achieve this in 2-agent, 1-resource allocation games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as the ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents. Copyright © 2012, Association for the Advancement of Artificial Intelligence. All rights reserved.

2012

Multi-Agent Learning for Resource Allocation Problems

Ludek Cigler

EPFL2013