My Math Forum Sequential game, how to derive utility functions.

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 November 29th, 2016, 09:53 AM #1 Newbie   Joined: Nov 2016 From: Stockholm Posts: 1 Thanks: 0 Sequential game, how to derive utility functions. Dear all, I am in the process of constructing a game theoretic model related to sanctions. We have two players, the sender (S) and the target (T). Discount factor delta. S chooses the sanction level (w). T chooses the action level (a). Utility of S is increasing in (a). Utility of T is decreasing in (a). Utilities of S and T are decreasing in (w). Hence, S will harm T and S by putting w(a), (w'(a)<0). Meanwhile, T chooses (a) conditional on w(a) (rational expectation). Player-specific harm is determined by two parameters in the utility functions. S chooses (w) at odd periods. T chooses (a) at even periods. I want to derive a utility function so that I can mathematically prove that the behaviour of the two players is rational. I suspect, however, that this will require dynamic programming. (I want to derive the utility function such that I can prove an equilibrium in which a(w) = w(a), i.e. the "response functions" match in equilibrium. In one sense, I want to parameterize this problem. Has anyone got a clue as to how to proceed doing this? I do not want to go by trial and error. Please see further information below (screenshot): https://gyazo.com/31aeb7bf005f182448f0262975c03ddd Thank you, and have a nice day. JF

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