An Agent-Based Adaptation of Friendship Games: Observations on Network Topologies

David S. Dixon

A friendship game in game theory is a network game in which a player’s immediate neighbors on the network are considered friends. Two friendship-based game models are examined: strategic complements and strategic substitutes. Strategic complements represent decisions for which it is preferable to do what one’s friends are doing, such as adopting a common software product. Strategic substitutes represent decisions for which it is preferable to let one friend act alone, such as the private provision of a public good. The game theory models predict the rate of change of preferences and specific equilibrium outcomes over specific time scales for each model. This paper employs an agent-based model (ABM) implementation of friendship games to examine the sensitivity of equilibrium states to network topology. In future work, the ABM model can provide a means to examine the motivations for behaviors of specific individuals in these models beyond closed-form payo functions.

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