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2's Action Player action for player Action I N Action Own Action Action Player l's Aumann best response cheap talk game cheap talk statement choose a best choose action complete information game cost of investing cost type invests cost type sends cost with probability dominant strategy electronic mail game failure of self-signalling Farrell and Rabin full revelation equilibrium game g game of figure high cost type incentive informed player interim expected utility invest equilibrium low cost type lowest type medium cost type mixed strategies Nash equilibrium one-sided incomplete information opponent to choose payoffs are given perfect Bayesian equilibrium played player games Player l's Action Player l's Type players have sent players invest positive probability preferred by player probability of investment pure strategy Rubinstein 1989 self-committing self-signalling condition sender solution concept Stackelberg action Stackelberg conditions Stephen Morris strategic complementarities two-sided incomplete information type of player type sends message types H underlying complete information