Optimal Equilibria of the Best Shot Game

17 Pages Posted: 5 Aug 2009

See all articles by Paolo Pin

Paolo Pin

Dipartimento di Economia Politica, Università degli Studi di Siena

Luca Dall' Asta

Abdus Salam International Centre for Theoretical Physics (ICTP)

Abolfazl Ramezanpour

Dipartimento di Fisica, Politecnico di Torino

Date Written: August 3, 2009

Abstract

We consider any network environment in which the 'best shot game' is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game will typically exhibit a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.

Keywords: networks, best shot game, simulated annealing

JEL Classification: C61, C63, D85, H41

Suggested Citation

Pin, Paolo and Dall' Asta, Luca and Ramezanpour, Abolfazl, Optimal Equilibria of the Best Shot Game (August 3, 2009). FEEM Working Paper No. 33.2009, Available at SSRN: https://ssrn.com/abstract=1443221 or http://dx.doi.org/10.2139/ssrn.1443221

Paolo Pin (Contact Author)

Dipartimento di Economia Politica, Università degli Studi di Siena ( email )

Piazza San Francesco 8
Siena, I53100
Italy

HOME PAGE: http://www.econ-pol.unisi.it/paolopin/

Luca Dall' Asta

Abdus Salam International Centre for Theoretical Physics (ICTP)

Strada Costiera 11
34100 Trieste
United States

Abolfazl Ramezanpour

Dipartimento di Fisica, Politecnico di Torino

Corso Duca degli Abruzzi, 24
Torino, Torino 10129
Italy

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