Associate Professor, Department of Economics
W.P. Carey School of Business, Arizona State University
Mechanism Design, Voting, Game Theory, Political Economy
Abstract: A proposer requires the approval of a veto player to change a status quo. Preferences are single peaked. Proposer is uncertain about Vetoer’s ideal point. We study Proposer’s optimal mechanism without transfers. Vetoer is given a menu, or a delegation set, to choose from. The optimal delegation set balances the extent of Proposer’s compromise with the risk of a veto. Under reasonable conditions, “full delegation” is optimal: Vetoer can choose any action between the status quo and Proposer’s ideal action. This outcome largely nullifies Proposer’s bargaining power; Vetoer frequently obtains her ideal point, and there is Pareto efficiency despite asymmetric information. More generally, we identify when “interval delegation” is optimal. Optimal interval delegation can be a Pareto improvement over cheap talk. We derive comparative statics. Vetoer receives less discretion when preferences are more likely to be aligned, by contrast to expertise-based delegation. Methodologically, our analysis handles stochastic mechanisms.
Extreme Points and Majorization: Economic Applications with Benny Moldovanu and Philipp Strack, Online Appendix, Econometrica, 2021, 1557-1593.
Abstract: We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. Finally, we apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.
Voting Agendas and Preferences on Trees: Theory and Practice with Benny Moldovanu, November 2020American Economic Journal: Microeconomics, forthcoming.
Abstract: We study how parliaments and other committees vote to select one out of several alternatives in situations where not all available options can be ordered along a “left-right” axis. Practically all democratic parliaments routinely use sequential binary voting procedures to select one of several alternatives. Which agendas are used in practice, and how should they be designed? We assume that preferences are single-peaked on an arbitrary tree and we study convex agendas where, at each stage in the sequential, binary voting process, the tree of remaining alternatives is divided into two subtrees that are subjected to a binary Yes-No vote. In this wide class of situations, we show that dynamic, strategic voting is congruent with sincere, unsophisticated voting, even if agents are privately informed and no matter what their beliefs about other voters are. We conclude the paper by illustrating the empirical implications of our results for two case studies from Germany and the UK.
Abstract: We study how a principal should optimally choose between implementing a new policy and maintaining the status quo when information relevant for the decision is privately held by agents. Agents are strategic in revealing their information and we exclude monetary transfers, but the principal can verify an agent’s information at a cost. We characterize the mechanism that maximizes the expected utility of the principal. This mechanism can be implemented as a cardinal voting rule, in which agents can either cast a baseline vote, indicating only whether they are in favor of the new policy, or they make specific claims about their type. The principal gives more weight to specific claims and verifies a claim whenever it is decisive.
Abstract: The main result in Daskalakis, Deckelbaum, and Tzamos (2017) establishes strong duality in the monopoly problem with an argument based on transportation theory. We provide a short, alternative proof using linear programming.
Abstract: We describe a remarkable instance of a motion-proposing and agenda-setting strategy by the Nazi party, NSDAP, during the Weimar Republic. Their purpose was to kill a motion of toleration of the new 1928 government, that would have allowed the government to continue in office without expressing confidence in it. The Nazi party was supported by their fiercest enemies on the far left, the communist party, but the combined killer strategy ultimately failed because of another agenda-setting counter-move undertaken by the Reichstag’s president. In order to understand and analyze that case we also briefly study killer amendments under various informational regimes and postulated voter behavior. In particular, the chances of success of killer amendments are shown to differ across several well-known binary, sequential voting procedures and across legislative agendas.
Abstract: We revisit the problem of a principal allocating an indivisible good with costly verification, as it was formulated and analyzed by Ben-Porath et al. (2014). We establish, in this setting, a general equivalence between Bayesian and ex-post incentive compatible mechanisms. We also provide a simple proof showing that the optimal mechanism is a threshold mechanism.
Abstract: A committee decides collectively whether to accept a given proposal or to maintain the status quo. Committee members are privately informed about their valuations and monetary transfers are possible. According to which rule should the committee make its decision? We consider strategy-proof and anonymous mechanisms and solve for the decision rule that maximizes utilitarian welfare, which takes monetary transfers to an external agency explicitly into account. For regular distributions of preferences, we find that it is optimal to exclude monetary transfers and to decide by qualified majority voting. This sheds new light on the common objection that criticizes voting for its inefficiency.
Abstract: We analyze sequential, binary voting schemes in settings where several privately informed agents have single-peaked preferences over a finite set of alternatives, and we focus on robust equilibria that do not depend on assumptions about the players’ beliefs about each other. Our main results identify two intuitive conditions on binary voting trees ensuring that sincere voting at each stage forms an ex-post perfect equilibrium. In particular, we uncover a strong rationale for content-based agendas: if the outcome should not be sensitive to beliefs about others, nor to the deployment of strategic skills, the agenda needs to be built ”from the extremes to the middle” so that more extreme alternatives are both more difficult to adopt, and are put to vote before other, more moderate options. An important corollary is that, under simple majority, the equilibrium outcome of the incomplete information game is always the Condorcet winner. Finally, we aim to guide the practical design of schemes that are widely used by legislatures and committees and we illustrate our findings with several case studies.
Abstract: In an independent private value auction environment, we are interested in strategy-proof mechanisms that maximize the agents’ residual surplus, that is, the utility derived from the physical allocation minus transfers accruing to an external entity. We find that, under the assumption of an increasing hazard rate of type distributions, an optimal deterministic mechanism never extracts any net payments from the agents, that is, it will be budget-balanced. Specifically, optimal mechanisms have a simple “posted price” or “option” form. In the bilateral trade environment, we obtain optimality of posted price mechanisms without any assumption on type distributions.
Working Papers / Work in Progress
Sequential Veto Bargaining with Incomplete Information with S. Nageeb Ali and Navin Kartik, March 2022
Abstract: We study sequential bargaining between a proposer and a veto player. Both have single-peaked preferences, but the proposer is uncertain about the veto player’s ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that there are also equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single-peaked preferences give the proposer an option to "leapfrog", i.e., to secure agreement from only low-surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design.
Abstract: We model a situation where ex ante opinions in a legislature are dichotomous but cross traditional left-right party lines, e.g., crucial decisions on ethical issues such as gay marriage and abortion, or joining/exiting an economic/political union. In addition to the two "extreme" positions on the left and on the right, we consider the effect of a compromise alternative whose location may be endogenous. We compare sequential, binary voting schemes conducted by privately informed agents with interdependent preferences: the voting process gradually reveals and aggregates relevant information about the location of preferred alternatives. The Anglo-Saxon amendment procedure (AV) always selects the (complete-information) Condorcet winner. In contrast, the continental successive procedure (SV) does not. This holds because AV allows learning about the preferences of both leftists and rightists, while SV only allows one-directional learning at each step. Moreover, under SV, the agenda that puts the alternative with ex ante higher support last elects the Condorcet winner more often than the agenda that puts that alternative first. The optimal compromise location for various goals is also shown to differ across voting procedures. We illustrate our main findings with a fascinating historical episode,the vote on the flag of the Weimar republic.
Older Working Papers
Abstract: We study general economies with indivisibilities in which agents can be producers and/or consumers of multiple units of heterogeneous goods and have substitutes preferences. We derive a simple tatonnement process from a steepest descent algorithm and use this process to construct an incentive compatible and efficient dynamic auction. This allows us to reinterpret the price adjustment process discovered by Ausubel (2006) as a steepest descent algorithm. Our results provide an incentive compatible and efficient dynamic auction for the substitutes and complements setting introduced by Sun and Yang (2006) and the trading network economy of Hatfield, Kominers, Nichifor, Ostrovsky and Westkamp (2013). We also provide a variant of this auction that uses only singleton demand reports.
Abstract: We study welfare-optimal decision rules for committees that repeatedly take a binary decision. Committee members are privately informed about their payoffs and monetary transfers are not feasible. In static environments, the only strategy-proof mechanisms are voting rules which are inefficient as they do not condition on preference intensities. The dynamic structure of repeated decision-making allows for richer decision rules that overcome this inefficiency. Nonetheless, we show that often simple voting is optimal for two-person committees. This holds for many prior type distributions and irrespective of the agents’ patience.