| Summary: | In this thesis we consider the problem of extending and adapting the classical Gambler's Ruin (GR) problem so that it can be played over net-works in a manner consistent with both the classical two-player and the fully connected N-player GR problem. We introduce an extended GR problem, in which players in a network compete against the opponents to whom they are connected, and in which players exit the network either when they achieve a specified target or when they become bankrupt. In both cases, the game continues with the remaining players. While a bankrupted player simply leaves the network, successful players (achievers) may produce one or more offspring who connect to the network and continue playing the game with a share of the achiever's resources. We simulate the extended GR problem in the case of contracting, fixed and evolving networks. A key motivation is to understand the interplay between the game and the network, i.e., how the topology of the network influences the progression of the GR problem game, and, conversely, how the game influences the evolution of the network topology. Therefore we consider several attachment rules, including random and preferential attachment. We also introduce a bespoke preferential attachment rule called kudos. Unlike the established preferential attachment rules, we find that kudos induces a phase transition in the network, as the size of target is varied.
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