The Evolutionary Stability of Bluffing in a Class of Extensive Form Games

It is common in many different organisms for contests to be settled through the use of agonistic displays rather than physical fights. For example, in contests where males compete for females, Red deer will settle the contest based on roaring tempo (Clutton-Brock and Albon 1979), toads on the pitch of a males croak (Davies and Halliday 1978) and African buffalo on ritualized head-on charges (Sinclair 1977). The traditional view of communication in agonistic encounters suggests that displays should contain information about who would win an escalated contest (i.e. Cullen 1972; Parker 1974). Exchanging this information would be benefical to both individuals, as they could settle the contest without the high cost of a fight. The recent concept of communication as exploitive (Krebs and Dawkins 1984) and the continuing application of game theory to aggressive encounters (Maynard Smith and Parker 1976; Bishop and Cannings 1978; Maynard Smith 1982; Enquist 1985), have stirred interest in the possiblity of bluffing (i.e. one individual gives false information in order to win a nonescalated contest). Maynard Smith (1982) reasoned that if bluffing did not have a high cost, it would invade, rendering a signal uninformative and eventually ignored by opponents. Along the same lines of reasoning, it has been argued that a display that affects the outcome of a cont st should transmit information about resource holding power (RHP) rather than information about intention (Maynard Smith 1974; Zahavi 1977, 1979). A signal correlated to RHP would be more costly to bluff and therefore contain more reliable information as compared to a signal of intention. The general predictions, therefore, hay been that displays will not contain information about intention and that bluffing will not be part of a stable strategy.