Nash Equilibria in Certain Two-Choice Multi-Player Games Played on the Ladder Graph

Victoria Sánchez Muñoz and Michael Mc Gettrick ()
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Victoria Sánchez Muñoz: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Ireland
Michael Mc Gettrick: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Ireland

International Game Theory Review (IGTR), 2021, vol. 23, issue 03, 1-23

Abstract: In this paper, we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with 2n players. We consider a set of games with generic payoff parameters, with the only requirement that a NE occurs if the players choose opposite strategies (anti-coordination game). The results show that for both, the ladder and circular ladder, the number of NE grows exponentially with (half) the number of players n, as NNE(2n) ∼ C(φ)n, where φ = 1.618.. is the golden ratio and Ccirc > Cladder. In addition, the value of the scaling factor Cladder depends on the value of the payoff parameters. However, that is no longer true for the circular ladder (3-degree graph), that is, Ccirc is constant, which might suggest that the topology of the graph indeed plays an important role for setting the number of NE.

Keywords: Graphical game; ladder graph; circular ladder; Nash Equilibrium (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0219198920500206

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