Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential signals that stochastically depend on the actual state of nature. These signal not only provide the players with partial information about the state of nature but also serve...

We study a class of symmetric strategic experimentation games. Each of two players faces a (exponential) two-armed bandit problem, and must decide when to stop experimenting with the risky arm. The equilibrium amount of experimentation depends on the degree to which experimentation outcomes are...

We consider an example of a Markov game with lack of information on one side, that was first introduced by Renault (2002). We compute both the value and optimal strategies for a range of parameter values.

We revisit well-known models of learning in which a sequence of agents make a binary decision on the basis of a private signal and additional information. We introduce efficiency measures, aimed at capturing the speed of learning in such contexts. Whatever the distribution of private signals, we...

We analyze a toy class of two-player repeated games with two-sided incomplete information. In effect, two players are facing independent decision problems and each of them holds information that is potentially valuable to the other player. We study to what extent, and how, information can be...

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure