Starting from an example of the Allies' decision to feint at Calais and attack Normandy on D-Day, this paper models misrepresentation of intentions to competitors or enemies. Allowing for the possibility of bounded strategic rationality and rational players' responses to it yields a sensible account of lying via costless, noiseless messages. In some leading cases, the model has generically unique pure-strategy sequential equilibria, in which rational players exploit boundedly rational players, but are not themselves fooled. In others, the model has generically essentially unique mixed-strategy sequential equilibria, in which rational players' strategies protect all players from exploitation.
Crawford, Vincent P..
2003."Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions ."American Economic Review,
93(1): 133-149.DOI: 10.1257/000282803321455197