# Monopoly Board Game Situation Modeled With Game Theory

Three players are playing the board game Monopoly. All properties are acquired, and only Player A has completed a color group. This also leaves Player A with very little cash. Player B and Player C could reasonably win only if they agree to a trade before Player A accrues enough cash to start building houses and eventually realizing exponential asset growth. Even if Players B and C knew they were on a clock, they could still rationally fail to reach a trade in time to have a reasonable chance of winning, if each holds out to get a better deal from the other.

With respect to Players B and C (treating Player A's actions as fixed and exogenous), does this situation exemplify brinkmanship or war of attrition? Canonical examples of brinkmanship typically include the possibility of immediate catastrophe, which does not seem to apply in terms of cash, but may apply in terms of probabilities of winning, if there is some critical mass of capital Player A could acquire beyond which their victory is virtually assured. Is it plausible that this situation is a war of attrition when utility is measured in dollars, but brinkmanship when utility is measured in probabilities of winning? When modeling these sorts of scenarios, should brinkmanship and war of attrition be assessed as separate games, or related to each other in some way (i.e., is one a special case of the other, or is it perhaps accurate to describe brinkmanship as a "war of attrition over epistemic probabilities of catastrophe")?

• Hi! I think the question would be improved if you were to greatly cut down on length and clarified the few definitions you used. For example, the entire Q could be something like this: In the context of bargaining, the conceptual relation between brinkmanship and war of attrition is puzzling me. Is one a special case of the other? Is it accurate to describe brinkmanship as a "war of attrition over probabilistic catastrophe"? If you want to, you can still provide an example, but I would make it a short well-defined game with actions, payoffs and probabilities. Jul 17, 2023 at 6:49
• That summary seems to cross the line from curation into omission, in light of what I'm trying to ask. The Monopoly scenario is not just an example; modeling it is the point of the question. The conceptual relation is mostly a stepping stone to get there. However, I will do my best to cut down the length and make that clear. Jul 17, 2023 at 19:06
• Oh no; if you actually want to model the Monopoly board game, I guess you would have to do away with these theoretical concepts and explain what your practical goal with modelling it is. Probably give more details about the game scenario. Jul 17, 2023 at 19:15