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Optimal Equilibria of the Best Shot Game


  • Luca Dall’Asta, Dipartimento di Fisica and Centre for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy, and Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri (Torino), Italy. Paolo Pin, Dipartimento di Economia Politica e Statistica, Universitá degli Studi di Siena, Piazza San Francesco 7, 53100 Siena, Italy ( Abolfazl Ramezanpour, Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.


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 typically exhibits 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. Finding such an equilibrium is a very hard task for any nontrivial 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 are unknown to the social planner.

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