Symmetric Subgame-Perfect Equilibria in Resource Allocation

Abstract

We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N -agent, C-resource allocation problems, where the resources are all homogeneous. Bhaskar proposed one way to achieve this in 2-agent, 1-resource 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 a ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the subgame-perfect equilibrium which implements 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.

Decentralized Anti-coordination Through Multi-agent Learning

“…In this paper, we did not address the issue of whether non-cooperative but rational agents would follow the protocol we outlined. In our other work (Cigler & Faltings, 2012), we address this issue and show that under certain conditions, the protocol can be implemented in Nash equilibrium strategies of the infinitely repeated resource allocation game.…”

“…Such a cost may already be implicit in the problem, such as the fact that wireless transmission costs energy, or it may be imposed by external payments. In our recent work (Cigler & Faltings, 2012), we show how this leads to equilibria where rational agents are indifferent between accessing the resource and yielding, and how these equilibria implement our allocation policy for rational agents. We consider this issue to be beyond the scope of this paper and refer the reader to our other work for a deeper analysis.…”