Strong implementation with partially honest individuals

In this paper we provide sufficient conditions for a social choice rule to be implementable in strong Nash equilibrium in the presence of partially honest agents, that is, agents who break ties in favor of a truthful message when they face indifference between outcomes. In this way, we achieve a relaxation in the condition of Korpela (2013), namely the Axiom of Sufficient Reason. Our new condition, Weak Pareto Dominance, is shown to be sufficient along with Weak Pareto Optimality and Universally Worst Alternative. We finally provide applications of our result in pure matching and bargaining environments

Bargaining through Approval

The paper considers two-person bargaining under Approval Voting. It first proves the existence of pure strategy equilibria. Then it shows that this bargaining method ensures that both players obtain at least their average and median utility level in equilibrium. Finally it proves that, provided that the players are partially honest, the mechanism triggers sincerity and ensures that no alternative Pareto dominates the outcome of the game

Partially-honest Nash implementation: a full characterization

A partially-honest individual is a person who follows the maxim, “Do not lie if you do not have to”, to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of n≥3 individuals, a social choice rule that can be Nash implemented is termed partially-honestly Nash implementable. The paper offers a complete characterization of the (unanimous) social choice rules that are partially-honestly Nash implementable. When all individuals are partially-honest, then any (unanimous) rule is partially-honestly Nash implementable. An account of the welfare implications of partially-honest Nash implementation is provided in a variety of environments

Treading a fine line: (Im)possibilities for Nash implementation with partially-honest individuals

This paper investigates the robustness of Dutta and Sen's (2012) Theorem 1 to weaker notions of truth-telling. It models individual i's honesty standard as a profile of (possibly non-empty) collections of ordered pairs of outcomes, one for each member of society, over which individual i feels truth-telling concerns. Individual i is honest provided that she states her true preferences as well as rankings (not necessarily complete) of outcomes that are consistent with the true preferences of individuals in her honesty standard. Under this notion of honesty, we offer a condition, called S(N)-partial-honesty monotonicity, which is necessary for Nash implementation when there are partially-honest agents. In an independent domain of preferences, we show that this condition is equivalent to Maskin monotonicity provided that honesty means stating the orderings of individuals (in a honesty standard) truthfully and individuals' honesty standards are non-connected

Natural implementation with partially honest agents in economic environments

In this paper, we introduce the weak and the strong notions of partially honest agents (Dutta and Sen, 2012), and then study implementation by natural price-quantity mechanisms (Saijo et al., 1996, 1999) in pure exchange economies with three or more agents in which pure-consequentialistically rational agents and partially honest agents coexist. Firstly, assuming that there exists at least one partially honest agent in either the weak notion or the strong notion, the class of efficient social choice correspondences which are Nash-implementable by such mechanisms is characterized. Secondly, the (unconstrained) Walrasian correspondence is shown to be implementable by such a mechanism when there is at least one partially honest agent of the strong type, which may provide a behavioral foundation for decentralized implementation of the Walrasian equilibrium. Finally, in this set-up, the effects of honesty on the implementation of more equitable Pareto optimal allocations can be viewed as negligible.

Essays on institutions and implementation

This thesis studies three issues in the field of implementation theory. In the first chapter, I examine the implementation of social choice rules under strong Nash equilibrium, when agents do not only care about the final outcomes, but also have a small intrinsic preference for honesty. Specifically, an agent is partially honest if she breaks ties in favour of a truthful strategy, when she faces indifference between outcomes. I present sufficient conditions for implementation in such cases and provide applications in matching and bargaining environments. In the second chapter, I study the issue of decentralization from the implementation perspective. In most cases of institution design, a social planner is forced to operate in a decentralized manner, by designing distinct institutions that deal with different issues or sectors, over which agents may have complementarities in their preferences. By utilizing the notion of a rights structure, I consider a two-sector environment and examine the possibilities that arise in implementation when the social planner can condition the rights structure of one sector to the one of the other. We distinguish two cases, one when a sector constitutes an institutional constraint (constrained conditional implementation), and one where both sectors can be objects of design (conditional implementation). I characterize the social choice rules that are implementable in the first case, while in the second case I provide sufficient conditions for implementation. My results outline the difficulties of implementation in decentralized environments. As applications, I include some possibility results. First I prove the implementability of a weaker version of the stable rule in a constrained matching environment with partners and projects and second, I prove the implementability of the weak Pareto rule in a multi-issue environment with lexicographic preferences. In the third chapter, I extend the positive results obtained in Dutta and Sen (2012) to the framework of rights structures. I show that the well-known unanimity condition is suffcient for implementation in such an environment when there is at least one partially honest agent

Implementation with evidence

We generalize the canonical problem of Nash implementation by allowing agents to voluntarily provide discriminatory signals, i.e. evidence. Evidence can either take the form of hard information or, more generally, have differential but non-prohibitive costs in different states. In such environments, social choice functions that are not Maskin-monotonic can be implemented. We formulate a more general property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation in economic environments. In some settings, such as when agents have small preferences for honesty, any social choice function is evidence-monotonic. Additional characterizations are obtained for hard evidence. We discuss the relationship between the implementation problem where evidence provision is voluntary and a hypothetical problem where evidence can be chosen by the planner as part of an extended outcome space.Mechanism design, costly signaling, verifiable information, Nash implementation

Complexity and repeated implementation

This paper examines the problem of repeatedly implementing an efficient social choice function when the agents’ preferences evolve randomly. We show that the freedom to set different mechanisms at different histories can give the planner an additional leverage to deter undesirable behavior even if the mechanisms are restricted to be simple and finite. Specifically, we construct a history-dependent sequence of simple mechanisms such that, with minor qualifications, every pure subgame perfect equilibrium delivers the correct social choice at every history, while every mixed equilibrium is strictly Pareto-dominated. More importantly, when faced with agents with a preference for less complex strategies at the margin, the (efficient) social choice function can be repeatedly implemented in subgame perfect equilibrium in pure or mixed strategies. Our results demonstrate a positive role for complexity considerations in mechanism design.Jihong Lee’s research was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A3A2043505) and by the Institute of Economic Research of Seoul National University. Hamid Sabourian gratefully acknowledges the hospitality and support from HKUST where part of this research was conducted.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jet.2015.05.00