Rodrigo A. Velez

Fairness and externalities

We study equitable allocation of indivisible goods and money among agents with other-regarding preferences. First, we argue that Foleys (1967) equity test, i.e., the requirement that no agent prefer the allocation obtained by swapping her consumption with another agent, is suitable for our environment. Then, we establish the existence of allocations passing this test for a general domain of preferences that accommodates prominent other-regarding preferences. Our results are relevant for equitable allocation among inequity-averse agents and in a domain with linear externalities that we introduce. Finally, we present conditions guaranteeing that these allocations are efficient.

Let them cheat

We consider the problem of fairly allocating a bundle of infinitely divisible goods among a group of agents with “classical” preferences. We propose to measure an agentʼs “sacrifice” at an allocation by the size of the set of feasible bundles that the agent prefers to her consumption. As a solution, we select the allocations at which sacrifices are equal across agents and this common sacrifice is minimal. We then turn to the manipulability of this solution. In the tradition of Hurwicz (1972), we identify, under some mild assumptions on preferences, the equilibrium allocations of the manipulation game associated with this solution when all commodities are normal: for each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation; conversely, each equilibrium allocation is equal-division constrained Walrasian. Furthermore, we show that if normality of goods is dropped, then equilibrium allocations may not be equal-division constrained Walrasian.

Sincere and sophisticated players in an equal-income market

We study the simultaneous direct revelation mechanism associated with each equal-income competitive social choice function in the allocation of objects and money among sincere and strategic agents. Strategic agents take advantage of sincere agents. They non-cooperatively coordinate on the equal-income competitive allocations for the true preferences that are Pareto undominated for them within the set of equal-income competitive allocations. Sincere agents are protected to some extent, however. Their welfare is usually above their maximin payoff.

Sharing an increase of the rent fairly

We characterize the family of non-contestable budget-monotone rules for the allocation of objects and money as those obtained by maximizing a maxmin social welfare function among all non-contestable allocations. We provide three additional seemingly independent approaches to construct these rules. We present three applications of this characterization. First, we show that one can “rectify” any non-contestable rule without losing non-contestability. Second, we characterize the preferences that admit, for each budget, a non-contestable allocation satisfying a minimal or maximal individual consumption of money constraint. Third, we study continuity properties of the non-contestable correspondence.

The price of imperfect competition for a spanning network

A buyer procures a network to span a given set of nodes; each seller bids to supply certain edges, then the buyer purchases a minimal cost spanning tree. An efficient tree is constructed in any equilibrium of the Bertrand game.

The costs and benefits of symmetry in common-ownership allocation problems

In experimental partnership dissolution problems with complete information, the divide-and-choose mechanism is significantly superior to the winners-bid auction. The performance of divide-and-choose is mainly affected by reciprocity issues and not by bounded rationality. The performance of the winners-bid auction is significantly affected by bounded rationality. Contrary to theoretical predictions divide-and-choose exhibits no first-mover bias.

Equitable rent division

How should a group of roommates allocate the rooms and contributions to rent in the house they lease? Economists have provided partial answers to this question in a literature that spans the last 40 years. Unfortunately, these results were developed in a non-linear fashion, which obscures them to the non-specialist. Recently, computer scientists have developed an interest in this problem, advancing from an algorithmic complexity perspective. With this new interest gaining traction, there is an evident need for a coherent development of the results in economics literature. This article does so. In particular, we build connections among results that were seemingly unrelated and considerably simplify their development, fill in non-trivial gaps, and identify open questions. Our focus is on incentives issues, the area in which we believe economists have more to contribute in this discussion.

Sincere and sophisticated players in the envy-free allocation problem

We study the problem of allocating a collective endowment of n objects among n agents when monetary compensation is available. We require budget balance and assume complete information. We also assume that money is desirable and that no object is infinitely better than another (in terms of money). Our preference domain contains, but is not restricted to, quasi-linear preferences. Examples are the dissolution of a partnership among partners who know each other well and the allocation of rooms and the division of the rent among housemates who collectively lease a house. An allocation is envy-free if no agent prefers the consumption of any other agent to her own consumption. We study the manipulation of the solutions that associate with each preference profile an envy-free allocation when some agents are sincere, i.e., unconditionally report their true preferences (and this is common knowledge), and the rest are strategic. (1) For each preference profile, the set of limit Nash equilibrium outcomes of the direct revelation game associated with each envy-free solution is the set of envy-free allocations, for the true preferences, that are not Pareto dominated for the strategic agents by another envy-free allocation. This implies that strategic agents take advantage, to some extent, of sincere agents. However, this has a limit. Strategic agents can only force a sincere agent to receive her worst envy-free allocation for the true preference profile. This allocation is generally better than the worst allocation she could receive if the reports of the strategic agents were not restricted by Nash behavior. (2) Independently of the envy-free solution that is operated, if there is at least another strategic agent, the worst case scenario equilibrium payoff for a strategic agent is equal to her worst case scenario equilibrium payoff if the agent were sincere. This suggests that given the opportunity to commit to unconditionally revealing her preferences, an agent may choose to do so even though her true preferences are not a dominant strategy. However, generically the best case scenario equilibrium payoff for a strategic agent is strictly better than the best case scenario equilibrium payoff if the agent were sincere. Thus, generically each agent may strictly prefer not to commit to unconditionally revealing her preferences, even when the agents true preference profile is a dominant strategy. An allocation is an equal income competitive allocation if there is a vector of prices that sustains the allocation as a competitive outcome in which each agent is endowed with an equal share of the aggregate income at the given prices. It is well known that in our environment the set of equal income competitive allocations coincides with the set of envy-free allocations. Thus, our results can be equally interpreted as the study of market manipulation in an environment with sincere and sophisticated agents. Even though no market solution is strategy-proof, the manipulation of each market solution results only in market outcomes with respect to true preferences. Moreover, in the presence of sincere agents, strategic agents manipulate the market and extract from sincere agents the maximum surplus they could unanimously agree on within the limits of the true-profile market outcomes.

Back to original frugality

We review recent research on frugality of mechanisms for the procurement of a spanning network. Frugality here is defined as the ratio of the maximum price that can be charged to the buyer in some equilibrium to the true minimal cost. Previous negative results are qualified under natural restrictions in costs.