In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-movers move. What properties of a game determine whether it has such negative value of information for a par
ticular player? Can a game have negative value of information for all players? To answer such questions, we generalize the definition of marginal utility of a good to define the marginal utility of a parameter vector specifying a game. So rather than analyze the global structure of the relationship between a games parameter vector and player behavior, as in previous work, we focus on the local structure of that relationship. This allows us to prove that generically, every game can have negative marginal value of information, unless one imposes a priori constraints on allowed changes to the games parameter vector. We demonstrate these and related results numerically, and discuss their implications.
We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hyste
resis effects. In particular, we show that by gradually imposing individual-specific tax rates on the players of the game, and then gradually removing those taxes, the players move from a poor equilibrium to one that is better for all of them.
In Newcombs paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based on that de
duction. Newcombs paradox is that game theory appears to provide two conflicting recommendations for what choice you should make in this scenario. We analyze Newcombs paradox using a recent extension of game theory in which the players set conditional probability distributions in a Bayes net. We show that the two game theory recommendations in Newcombs scenario have different presumptions for what Bayes net relates your choice and the algorithms prediction. We resolve the paradox by proving that these two Bayes nets are incompatible. We also show that the accuracy of the algorithms prediction, the focus of much previous work, is irrelevant. In addition we show that Newcombs scenario only provides a contradiction between game theorys expected utility and dominance principles if one is sloppy in specifying the underlying Bayes net. We also show that Newcombs paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its `prediction after you make your choice rather than before.
In Newcombs paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice, and fills th
e two boxes based on that deduction. Newcombs paradox is that game theorys expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. A recent extension of game theory provides a powerful tool for resolving paradoxes concerning human choice, which formulates such paradoxes in terms of Bayes nets. Here we apply this to ol to Newcombs scenario. We show that the conflicting recommendations in Newcombs scenario use different Bayes nets to relate your choice and the algorithms prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcombs paradox, the focus of much previous work, is irrelevant. We similarly show that the utility functions of you and the antagonist are irrelevant. We end by showing that Newcombs paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its `prediction emph{after} you make your choice rather than before.
