This thesis is an examination of the traveler’s dilemma and its backward induction argument. I begin by explaining relevant terminology, the prisoner’s dilemma, and the iterated prisoner’s dilemma; the discussion of which aids my examination of the traveler’s dilemma and its backward induction argument. My evaluation of the traveler’s dilemma involves a dissection of the game into its different components, a presentation of the salient similarities and differences between the traveler’s dilemma and the prisoner’s dilemma, and the exploration of three possible solutions. The first two solutions are adapted from ones initially created to solve other backward induction argument problems. The third solution is original and its foundation rests on the unique structure of the traveler’s dilemma. I focus on this third solution and consider several objections to it. I end this thesis with some ancillary comments about the possibility of generalizing the third solution to other backward induction argument problems. / February 2008

This thesis is an examination of the traveler’s dilemma and its backward induction argument. I begin by explaining relevant terminology, the prisoner’s dilemma, and the iterated prisoner’s dilemma; the discussion of which aids my examination of the traveler’s dilemma and its backward induction argument. My evaluation of the traveler’s dilemma involves a dissection of the game into its different components, a presentation of the salient similarities and differences between the traveler’s dilemma and the prisoner’s dilemma, and the exploration of three possible solutions. The first two solutions are adapted from ones initially created to solve other backward induction argument problems. The third solution is original and its foundation rests on the unique structure of the traveler’s dilemma. I focus on this third solution and consider several objections to it. I end this thesis with some ancillary comments about the possibility of generalizing the third solution to other backward induction argument problems.

This thesis is an examination of the traveler’s dilemma and its backward induction argument. I begin by explaining relevant terminology, the prisoner’s dilemma, and the iterated prisoner’s dilemma; the discussion of which aids my examination of the traveler’s dilemma and its backward induction argument. My evaluation of the traveler’s dilemma involves a dissection of the game into its different components, a presentation of the salient similarities and differences between the traveler’s dilemma and the prisoner’s dilemma, and the exploration of three possible solutions. The first two solutions are adapted from ones initially created to solve other backward induction argument problems. The third solution is original and its foundation rests on the unique structure of the traveler’s dilemma. I focus on this third solution and consider several objections to it. I end this thesis with some ancillary comments about the possibility of generalizing the third solution to other backward induction argument problems.

This dissertation explores the importance of the payoff structure and beliefs for noncooperative games. Chapter 2 considers instances where the payoffs and the objectives may not be very clear to the players or the analyst. We develop a model for analyzing such games using a vector of reference utilities which are included in the definition of the game and assumed to be shared by all players. These are used to obtain the true utilities in the game. Conditions for the existence of equilibrium are identified by allowing players to have beliefs about the others. The solution concept is applied to the Traveler's Dilemma and a duopoly. In Chapter 3 a non-cooperative model of network formation is developed. Agents form links based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents without their consent, provided the agent forming the link makes the appropriate investment. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity by allowing for different failure probabilities. We investigate Nash networks that exhibit connectedness and redundancy and provide an explicit characterization of star networks. Efficiency and Pareto-optimality issues are discussed through examples. We also explore the consequences of three alternative specifications which address criticisms of such communication networks. Chapter 4 examines noncooperative fuzzy games. Both in fuzzy noncooperative games and in abstract economies, players impose mutual restrictions on their available strategic choices. Here we combine these two theories: A player tries to minimize the restrictions he imposes on others, while respecting the restrictions imposed by others on him, but does not explicitly pursue any other objectives of his own. We establish existence of an equilibrium in this framework. In Chapter 5 normal form game is modeled using tools from fuzzy set theory. We extend the decision theory framework of Bellman and Zadeh (1970) to a game-theoretic setting. The formulation is preliminary / Ph. D.