Decision analysis in competitive and cooperative environments

This thesis contains three chapters in which we axiomatically analyze individual and collective decision problems in competitive and cooperative environments. In Chapter 1, we give a general introduction. In Chapter 2, we propose a theory of revealed preferences that allows both the status-quo bias and indecisiveness between any two alternatives. We extend a standard choice problem by adding a status-quo alternative and we incorporate standard choice theory as a special case. We characterize choice rules that satisfy two rationality requirements, status-quo bias, and strong SQ-irrelevance. In Chapter 3, we analyze bargaining situations where the agents' payoffs fromdisagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash. On our extended domain, we analyze the implications of two central properties which, on the Nash domain, are known to be incompatible: strong monotonicity and scale invariance. We characterize bargaining rules that satisfy strong monotonicity, scale invariance, weak Pareto optimality, and continuity. In Chapter 4, we analyze markets in which the price of a traded commodity is fixed at a level where the supply and the demand are possibly unequal. The agents have single peaked preferences on their consumption and production choices. For such markets, we analyze the implications of population changes as formalized by consistency and population monotonicity properties. We characterize trade rules that satisfy Pareto optimality, no-envy, and consistency as well as population monotonicity together with Pareto optimality, no-envy, and strategy-proofness

Revealed incomplete preferences under status-quo bias

We propose a theory of revealed preferences that allows both the status-quo bias and indecisiveness between any two alternatives

Production economies with single peaked preferences: pareto optimal and strategy proof rules

We analyze production economies with a linear technology and single peaked preferences. We first characterize the class of Pareto optimal (allocation) rules. We then characterize the subclass that additionally satisfies strategy proofness. Finally, we show that a uniform production rule uniquely satisfies Pareto optimality, strategy proofness, and equal treatment of equals. A similar result is obtained if equal treatment of equals is replaced with stronger fairness properties such as no-envy or anonymity. Our results can be applied to the problem of allocating central government funds among regional development agencies

Bargaining with nonanonymous disagreement: monotonic rules

We analyze bargaining situations where the agents’ payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash (1950). On our extended domain, we analyze the implications of two central properties which, on the Nash domain, are known to be incompatible: strong monotonicity (Kalai, 1977) and scale invariance (Nash, 1950). We first show that a class of monotone path rules uniquely satisfy strong monotonicity, scale invariance, weak Pareto optimality, and “continuity”. We also show that dropping scale invariance from this list characterizes the whole class of monotone path rules. We then introduce a symmetric monotone path rule that we call the Cardinal Egalitarian rule and show that it is weakly Pareto optimal, strongly monotonic, scale invariant, symmetric and that it is the only rule to satisfy these properties on a class of two-agent problems

A mechanism design approach to allocating central government funds among regional development agencies

To allocate central government funds among regional development agencies, we look for mechanisms that satisfy three important criteria: efficiency, (individual and coalitional) strategy proofness (a.k.a. dominant strategy incentive compatibility), and fairness. We show that only a uniform mechanism satisfies all three. We also show that all efficient and strategy proof mechanisms must function by assigning budget sets to the agencies and letting them freely choose their optimal bundle. In choosing these budget sets, the agencies’ private information has to be taken into account in a particular way. The only way to additionally satisfy a weak fairness requirement (regions with identical preferences should be treated equally) is to assign all agencies the same budget set, as does the uniform mechanism. Finally and maybe more importantly, we show that the central government should not impose constraints on how much to fund an activity (e.g. by reserving some funds only for a particular activity): otherwise, there are no efficient, strategy proof and fair mechanisms, no matter how small these constraints are