Bluffing Beyond Poker (Johannes Horner, Nicolas Sahuguet)

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that player 2 achieves in the original P.B.E., regardless of valuation. In the subgame
following the deviation by player 2: Player 1 s with valuations v 2 (�; 1] play against
player 2s with w 2 (�; 1] . In this subgame, player 2 with valuation �+ (a valuation
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arbitrarily close to � from above) can achieve pro& t K; only if
1��
1��
� � �
� � = K.
1 � �
Hence, the equilibrium with assured deterrence is a P.S.E. if and only if such a � 2 (0; 1)
cannot be found. Since the left-hand side is increasing in �, it is both necessary and
su�cient that
1��
1��
� � � e�(1��) � � �
lim � � = 5 :
�!1
1 � � 1 � � 1 + �
1�K
The latter inequality can be rewritten as 1 + � ln2K = 0; which precisely states
1�2K
�
that K = K. Finally, when K > 1=2, there is no equilibrium with assured deterrence,
since when K meets this condition there is no value of � in the open unit interval
which satis& es � = K= (1 � K) Finally, equilibria with covering, as speci& ed in the
�
text for K
the equilibrium path .
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References
[1] Amann, E., and W. Leininger, Asymmetric all-pay auctions with incomplete in-
formation: the two-player case, Games Econ. Behav. 14 (1996), pp. 1-18.
[2] Bellman, R., and D. Blackwell, Some two-person games involving blu�ng, Proc.
Natl. Acad. Sci. 35 (1949), pp. 600-605.
[3] Binmore, K., Fun and Games: A text on Game Theory , D.C. Heath and Co.,
Lexington, MA, 1992.
[4] Bishop, D.T., C. Cannings, A Generalised War of Attrition, J. Theoret. Biol. 70
(1978), pp. 85-124.
[5] Borel, E.,
[6] Dixit, A., Strategic Behavior in Contests, American Economic Review, 77 (5),
(1987), pp. 891-8.
[7] Gibson, B., and Sachau, D., Sandbagging as a Self-Presentational Strategy: Claim-
ing to Be Less Than You Are, Personality and Social Psychology Bulletin, 26 (1),
(2000), pp. 56-70.
[8] Grossman, S., and M. Perry, Perfect Sequential Equilibrium, J. Econ. Theory 39
(1986), pp. 97-119.
[9] Karlin, S., and R. Restrepo, Multistage poker models , Annals of mathematics
studies No. 39, Edited by M. Dresher, A. W. Tucker, and P. Wolfe, Princeton
Univ. Press, Princeton, 1957.
[10] Maynard Smith, J., The Theory of Games and the Evolution of Animal Con! icts,
J. Theoret. Biol. 47 (1974), pp. 209-221.
[11] Maynard Smith, J., Evolution and the Theory of Games , Cambridge University
Press, Cambridge, U.K., 1982
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[12] McAfee, P. and K. Hendricks, Feints, Mimeo, University of Texas, 2001.
[13] McDonald, J., Strategy in Poker, Business and War , Norton, New York, NY,
1950.
[14] Myerson R., Optimal Auction Design, Math. Oper. Res. 6 (1981), pp. 58-73.
[15] Nash, J. and L. Shapley, A Simple Three-Person Poker Game, in Dimand M.A,
Dimand R., eds. The foundations of game theory. Volume 2. Elgar Reference
Collection. Cheltenham, U.K. and Lyme, N.H.: Elgar; 1997, pp. 13-24. Previously
published: [1950].
[16] Newman, D.J., A model for real poker, Operations Research 7 (1959), pp. 557-560.
[17] Riechert, S.E., Games Spider Play: Behavioural Variability in Territorial Disputes,
Behav. Ecol. Sociobiol. 3, (1978), pp. 135-162.
[18] Sakai, S., A model for real poker with an upper bound of assets, J. Optim. Theory
Appl. 50 (1986), pp. 149-163.
[19] Rosen, S., Prizes and Incentives, American Economic Review, 76 (4), (1986), pp.
716-727.
[20] Shepperd, J.A. and R.E. Socherman, On the Manipulative Behavior of Low Machi-
avellians; Feigning Incompetence to Sandbag an Opponent, Journal of Person-
ality and Social Psychology, 72 (1997), pp. 1448-1459.
[21] Von Neumann, J. and O. Morgenstern, Theory of Games and Economic Behav-
ior , Princeton Univ. Press, Princeton, 1944.
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