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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Victoria Sánchez Muñoz & Michael Mc Gettrick, 2021. "Nash Equilibria in Certain Two-Choice Multi-Player Games Played on the Ladder Graph," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-23, September.
    • Handle: RePEc:wsi:igtrxx:v:23:y:2021:i:03:n:s0219198920500206
    DOI: 10.1142/S0219198920500206
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