Dynamic tournaments and strategic games.

Summary The thesis is structured around three chapters in theoretical economics and non-cooperative game theory. The first two chapters, although independent, deal with competitive situations between economic agents that take place over several periods of time called tournaments. In the first chapter, we look for the conditions under which it is optimal for the principal to give the agents a logit probability of winning. This probability of winning is therefore endogenous and corresponds to the number of optimal monitoring periods for the principal. In the second chapter, we give the tournament administrator the possibility to choose the bonus allocation mechanism (for example by choosing the composition of a committee). In particular, we show that the bonus to be given to the winner is minimized when the random allocation mechanism of the prize does not always reward the most productive agent over all the T-periods of the competition. The third chapter is set in the framework of non-cooperative game theory and deals with the epistemic justification of concepts prevalent to the coordination of players on a particular set of strategies called the p-best response set, the iterated p-dominant Nash equilibrium and the Curb set. In particular, we assume that players have p-beliefs about the amount of prudence of their opponent and at the same time believe that the opponent is a maximizing agent of his subjective expected utility. We show that players satisfy these assumptions if and only if they choose strategies restricted to a certain class of so-called p-best sets.