We consider a group of voters that needs to decide between two candidates. We propose a novel family of neutral and strategy-proof rules, which we call sequential unanimity rules. By demonstrating their formal equivalence to the M-winning coalition rules of Moulin (1983), we show that sequential unanimity rules are characterized by neutrality and strategy-proofness. We establish our results by developing algorithms that transform a given M-winning coalition rule into an equivalent sequential unanimity rule and vice versa. The analysis can be extended to accommodate the full preference domain in which voters may be indifferent between candidates.
We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed win-lose dependent transfers, in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.
We consider a setting where each player of a normal-form game privately designs an information structure before playing the game. One of these designs is chosen at random to determine the distribution of the private messages that players receive. These messages allow players to correlate their actions; however, private information design implies a push from correlated to Nash equilibria. Indeed, the sequential equilibrium payoffs of the private information design extensive-form game are correlated equilibrium payoffs of the underlying normal-form game, but not all correlated equilibrium payoffs are sequential equilibrium payoffs. In generic 2-player games, the latter are specific convex combinations of two Nash equilibrium payoffs. In any 2-player game, imposing optimal beliefs from private information design allows us to obtain sufficient epistemic conditions for Nash equilibrium that require only knowledge of players' rationality.
We study priority-based matching markets with public and private endowments. We show that efficiency-adjusted deferred acceptance (EADA) is justified-envy minimal in the class of efficient mechanisms, while Top trading cycles (TTC) and other popular mechanisms are not. Our findings highlight EADA as an interesting alternative to TTC in the context of transplantation-organ markets. Restricting attention to strategyproof mechanisms, we show that TTC is justified-envy minimal, strengthening the result of Abdulkadiroglu et al. (2020).
In a game in extensive form, we say that a sequence of trembles destabilizes an outcome if there is no corresponding sequence of payoff perturbations and Nash outcomes converging to the outcome. We use equilibrium destabilization to characterize sequential equilibria and sequentially stable outcomes, and to reinterpret standard selection criteria in signaling games as a means of ruling out implausible equilibria by identifying destabilizing tremble sequences. We show that the existence of a maximally destabilizing sequence of trembles (destabilizing all outcomes but one) significantly simplifies studying strategically stable behavior in complex games such as finitely repeated games.
By showing that a one-shot deviation property holds for almost all large games with i.i.d. randomly drawn payoffs in which a convention (in the sense of Young, 1993a) exists, long-run outcomes under behavioral rules are characterized by social choice rules.
In school choice problems, the pursuit of student welfare (efficiency) is constrained by the requirement to respect schools’ priorities (fairness). Among fair matchings, even the welfare maximizing one, the Student-Optimal Stable Matching (SOSM), is inefficient. Moreover, any mechanism that yields welfare gains over the SOSM is manipulable by students. This paper investigates the fairness and incentive properties of efficient mechanisms. We compare matchings using the notion that one matching is less unfair than another if it generates a smaller set of students whose priorities are violated, and we define minimal unfairness accordingly. We show that the Efficiency-Adjusted Deferred Acceptance (EADA) mechanism is minimally unfair within the class of Pareto efficient mechanisms satisfying a simple incentive requirement, top-manipulation-proofness. Moreover, the EADA satisfies a stronger property, upper-manipulation-proofness. Upper-manipulation-proofness is a broad incentive property one can maintain while improving upon the SOSM. Together, these results highlight a sharp frontier in school choice: when the objective is efficiency and improving student welfare over the SOSM, the EADA emerges as a compelling mechanism in both fairness and incentive terms.
We prove a Folk theorem when players with bounded rationality learn as they play a repeated potential game. We use a dynamic generalization of smooth fictitious play with bounded $m$-memory strategies to model learning with bounded rationality that is consistent with learning by algorithms. In a repeated potential game with perfect monitoring, we use this learning model to show that for any feasible and individually rational payoff profile, if players have sufficient memory, are sufficiently patient, and best respond with sufficiently few mistakes, then the players have a non-zero probability of learning an $m$-memory strategy profile that achieves an average payoff close to the specified payoff profile for an appropriate continuation game. Moreover, the strategy profile learned is an $m$-memory $\epsilon$-subgame perfect equilibrium of the repeated game. This finding demonstrates that competition authorities are correct in their concern about algorithmic collusion.
This paper analyzes the extent to which well-known results on the relationship between the bargaining set, the core, and the kernel in one-to-one assignment games generalize to many-to-one assignment markets, and by extension, many-to-many markets. Using a minimal counterexample, we show that the bargaining set does not necessarily coincide with the core and that the kernel may not be contained within the core. We would like to highlight that the failure of the coincidence between the core and the bargaining set, as observed in the many-to-one assignment game, is quite notable. This is especially true when compared to various other highly structured games, many of which emerge from combinatorial optimization problems, such as the one underlying many-to-one assignment games.
We analyze risk-taking behaviors of financial institutions linked through cross-shareholding relationships. We endogenize risk exposure accounting for default risk by modeling Value-at-Risk-based risk-management – that is targeted default probabilities – in the presence of extreme risk on asset return. We relate risk-taking behaviors to a centrality measure that captures the propagation of losses within the network, and show that network integration increases risk-taking levels and expected return. However, we show that network integration also results in larger expected shortfall, indicating greater exposure to losses for creditors. We explore the impact of the cross-shareholding network on the implementation of regulation, particularly through capital requirements, and identify key institutions, those with the highest influence on aggregate investments in risky assets.
Parties in primary elections often choose between candidates who appeal to their base and those who appeal to the broader electorate. I present a model of primaries where incumbents can exploit this trade-off the opposition faces between ideological congruence and electability. In the model, incumbents reduce their appeal to the median voter by moving away from the center. In doing so, they provoke the opposition into nominating extremists, improving their reelection prospects. This mechanism generates elite polarization as politicians leapfrog voters — not despite electoral concerns, but because of them. The analysis fits the observation that incumbents sometimes move away from the center near the end of their term. Provoking the opposition relies on two conditions: divergence of primary and general electorates and a limited set of potential nominees. I argue that partisan sorting and changes in nomination procedures over the last decades made this strategy viable.
Economists often rely on people’ s choices to infer their preferences. However, inferring preferences from choices becomes problematic when people face unobserved constraints. In this paper, I study how to (cautiously) infer preferences from choices when the choices of the members of a social group are subject to a constraint that we only imperfectly know. When this happens, heterogeneity in the group’ s choices, along with more information about the constraint, helps recover the preferences of group members, whereas homogeneity in choices hinders it. I further argue that standard approaches to choice-based welfare analysis can lead to misleading inferences about welfare when there are unobserved social constraints.
This paper analyzes the welfare properties of the mechanism Taiwan uses to match students to high schools. I study the Taiwan mechanism under a theoretical model where students share the same ordinal rankings, and a single lottery determines schools’ preferences. In this setting, all Taiwan mechanisms ex ante weakly Pareto dominate deferred acceptance for strategizing students. Additionally, in my model, there always exists a Taiwan mechanism that provides greater welfare than deferred acceptance to students who do not strategize. Using Cambridge Public School data, I demonstrate that the Taiwan mechanism outperforms deferred acceptance for a range of deduction rules.
We consider a market with indivisible objects, called houses, and monetary transfers. Each house is initially occupied by one agent and each agent demands exactly one house. The problem is to identify the complete set of direct allocation mechanisms that can be used to reallocate the houses among the agents. On the one hand, for price eq1uilibrium mechanisms, we show that the only non-manipulable mechanism is one with a minimum equilibrium price vector. The result is not true on the classic or the quasi-linear domains, but on reduced domains of preference profiles containing “almost all” profiles in the classic or the quasi-linear domain, respectively. On the other hand, while minimum price equilibrium mechanisms are not necessarily efficient (as prices are not zero), we show that no non-manipulable mechanism Pareto dominates a minimum price equilibrium mechanism, making them constrained efficient in the class of non-manipulable mechanisms.
We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent’s marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.
In this paper, we explore the issue of manipulability in the setting of financial systems by considering two weak forms of immunity: merging-proofness and splitting-proofness. Not surprisingly, splitting-proofness conflicts with basic requirements such as the priority of debt over equity and the limited liability of equity. Remarkably, we provide a comprehensive characterization of the class of bankruptcy rules that gives rise to financial rules that satisfy merging-proofness.
Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets of preferences. We apply these theorems to derive new comparative statics theorems for collective choice and under analyst uncertainty, and to characterise a general 'maxmin' class of uncertainty-averse preferences over Savage acts.
We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today’s partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players’ expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value.