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Portfolio competitions and rationality
Kuběna, Aleš Antonín ; Šmíd, Martin
We study investment competitions in which the players with highest achieved returns are rewarded by fixed prizes. We show that, under realistic assumptions, a game the participants play lacks a pure equilibrium and that the ``max-min'' solution of the game lies in one of the extremal points of the feasible set, namely in the one having maximal probability that the portfolio return falls into its normal cone. We analyse empirically a portfolio competition held recently by the Czech portal ``lidovky.cz''; we find that the majority of people do not behave according to the game-theoretic conclusions. Consequently, searching for factors influencing a choice of particular stocks, we find that that the only significant determinant of the choice is a size of the stock's issuer.
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Pexeso ("Concentration game") as an arbiter of bounded-rationality models
Kuběna, Aleš Antonín
Among board games, Pexeso (Concentration game) for two players is a game almost purely output-oriented, i.e. the optimal play is not given by strategic plans with long-term horizon (e.g. no short-term tactical sacrifice is observed). So, the optimal strategy and game dynamics may be calculated almost analytically, assuming a given rationality restrictions of the players. In the paper, the optimal strategy for two players is solved using dynamic programming. Further, it is proved that for rational players, the game would end with ”stalemate” (the game never ends) with a probability close to 1. Further, the game dynamics is described if a rationality restriction is given such that the players perform a random move instead of the optimal one with probabilities P,Q > 0. In this case, the probability of a stalemate is equal to zero.
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