Credible Threats

Game Theory · Axiom Academy

Unit 3: Sequential Games - Understanding what makes threats believable and strategically effective 1. What Makes a Threat Credible? The key question is: "Would you actually do it?" A threat is only effective if your opponent believes you will follow through. In game theory, we assume rational players will only execute threats that serve their own interests when the time comes. "If you enter my market, I will lower prices to compete." Why credible? Lowering prices is profit-maximizing when facing competition. "If you enter my market, I will give away products for free." Why not credible? Giving away products loses money regardless of competitor's actions. 2. Entry Deterrence: A Classic Example Consider an incumbent firm (Firm I) facing a potential entrant (Firm E). The entrant decides whether to enter the market, and if entry occurs, the incumbent decides whether to fight (aggressive pricing) or accommodate (share the market). If E stays out: I gets 10, E gets 0 If E enters and I accommodates: I gets 5, E gets 5 If E enters and I fights: I gets 2, E gets -1 The incumbent would like to threaten: "If you enter, I will fight!" But is this credible? Analysis: If entry actually occurs, the incumbent must choose between fighting (payoff = 2) and accommodating (payoff = 5). A rational incumbent prefers 5 over 2, so they will accommodate. 3. When Threats Become Credible Now consider a modified scenario where the payoffs change if the incumbent has already invested in excess capacity:

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