Essays in Microeconomic Theory

This dissertation contains various results in game theory and search. Chapter 1 considers the effect of obtaining experience in the problem of search and experimentation. Chapter 2 studies penalty card strategies in repeated games. Chapter 3 is devoted to explicit renegotiation in repeated games.;Chapter 1 studies effect of obtaining experience in the environment of a multi-armed bandit on the experimentation behavior of an agent. When the agent pulls an arm, she learns the payoff generated by this arm. However, there is another effect: the agent becomes better at pulling the arm, which leads to better payoff. The effect of agent becoming better, or experienced, in pulling the arm is studied in the decision problem of a single agent, and in the dynamics in case of many agents. It is shown that the experience effect reduces the agents' incentives to experiment. The effect of experience reducing experimentation is non-monotone in the rate of acquiring experience. For the case of many agents setting, it is shown that under some conditions the agents who obtain experience at higher rate, may be less willing to experiment with new options.;Chapter 2 studies repeated games with players having private types. Private types change with time according to a time homogeneous Markov chain, independently across players. Players are prescribed to report their private types truthfully, and then the related efficient action profile is prescribed. In order to incentivize players to report truthfully, penalty card strategies are considered. With these strategies if a player reports a type which makes the payoff of others low, that player may obtain a penalty card. There is a limit on number of penalty cards for each player, and if that limit is reached, that player goes on suspension for some time. While being on suspension, the player's payoff is not taken into account when choosing an efficient action profile. After suspension duration ends, one card is removed and the player is back in the game. It is shown that under some mild conditions on players' payoffs it is possible to achieve efficiency with penalty card strategies if players are patient enough. With penalty card strategies simple statistics on amount of penalty cards and identities of players on suspension are used, as compared to history of all previous reports.;Chapter 3 studies explicit renegotiation in repeated games with two players. In each period there are two stages: action stage and renegotiation stage. During renegotiation stage one of the players can propose to change the current plan of future actions to a new one; and if the other player agrees, they indeed implement the new plan. Under this assumption a set of achievable payoff is sought. Necessary and sufficient conditions are derived for the payoff to be achieved in equilibrium. Each condition takes form of an orthant.