This appendix contains the analysis of the general version of the Asymmetric Escalation Game with incomplete information, introduced in chapter 6 and section 9.2, and specified in section A1.4. (See also figures 6.3 and A1.7.) Recall that the twenty relevant parameter values satisfy 0 < pCh < 1, 0 < pHH, 0 < pHS, 0 < pSH, 0 < pSS, pHH + pHS+ pSH + pSS = 1, cEE− < cDE < cEE+ < cDD < cED < cSQ < cDC, and dEE− < dED < dEE+ < dDD− < dDC < dDD+ < dDE < dSQ.

As usual, player Challenger is strategically Hard, i.e., Challenger's utility for outcome EE is cEE+, with probability pCh; otherwise, Challenger is strategically Soft, i.e., Challenger's utility for outcome EE is cEE−, with probability 1 – pCh. Player Defender is said to be strategically Hard when its utility for outcome EE is dEE+ ; otherwise Defender is strategically Soft and has utility dEE− for outcome EE. As well, Defender is either tactically Hard, with utility dDD+ for outcome DD, or tactically Soft, with utility dDD− for DD. Defender's credibility parameters are interpreted as follows: with probability pHH, Defender is both tactically and strategically Hard; with probability pHS, Defender is tactically Hard but strategically Soft; with probability pSH, Defender is tactically Soft but strategically Hard; and with probability pSS, Defender is both tactically and strategically Soft. For convenience, we repeat here the definitions of the thresholds (see section A2.4 for more details).