Second International Conference “Mathematics Days in Sofia”
July 10–14, 2017, Sofia, Bulgaria
Biased Coin Toss and Nash Equilibrium
Peter Dragnev1 , David Benko2 , Dan Coroian3 ,
Ramon Orive4
1
Indiana University–Purdue University Fort Wayne, USA
[email protected]
2
3
University of South Alabama, USA
Indiana University–Purdue University Fort Wayne, USA
4
University La Laguna, Santa Cruz de Tenerife, Spain
This is an approximation theory/game theory approach to a biased coin game
(P (heads) = p) with two players, where the coin is tossed n times. One of
the players chooses n + 1 numbers ai to estimate the p based on each outcome
observed. The penalty payoff is |p−ai |. The player tries to minimize the expected
payoff. The second player tries to select p that will maximize this expected payoff
regardless of the choice ai of the first. Best strategies satisfy Nash equilibrium
and the maximum likelihood is not the top strategy.