Appendix A - Mathematical Proofs to Chapter 3

Summary

Definition: Formally, the Transition with Secret Information (TSI) game is defined by N = {A,O} the set of players, where O, the opposition, is the Receiver and A, the autocrats, are the Sender, who has private information about the parameter i affecting and O and A's payoffs;

i ~ u[0,1] is A's private information about infiltration levels; O knows that i is uniformally distributed;

E(i) is the expected value of i based on O's prior belief about the distribution of i

μ (i|m) is O's a posterior belief about i after having observed A's action, m

M : [0,1] → {Negotiate, SQ} is the set of A's strategies;

R : {Negotiate, SQ} → {refuse, renege, honor} is the set of O's strategies;

N_A, N_O represent payoffs to A and O, respectively, associated with the status quo;

n_A, n_O represent payoffs to A and O, respectively associated with A's action to negotiate and O's action to refuse;

t_A, t_O represent payoffs to A and O, respectively, associated with A's action to negotiate and O's action to honor;

i, 1−i represent payoffs to A and O, respectively, associated with A's action to negotiate and O's action to renege;