The inefficiency of selfish routing in congested networks is a classical problem in algorithmic game theory, often captured by the Price of Anarchy (i.e., the ratio between the social cost of decentralized decisions and that of a centrally optimized solution.) With the advent of autonomous vehicles, capable of receiving and executing centrally assigned routes, it is natural to ask whether their deployment can eliminate this inefficiency. At first glance, a central authority could simply compute an optimal traffic assignment and instruct each vehicle to follow its assigned path. However, this vision overlooks critical challenges: routes must be individually rational (no vehicle has an incentive to deviate), and in practice, multiple planning agents (e.g., different companies) may coexist and compete. Surprisingly, we show that such competition is not merely an obstacle but a necessary ingredient for achieving optimal outcomes. In this work, we design a routing mechanism that embraces competition and converges to an optimal assignment, starting from the classical Pigou network as a foundational case.

This paper considers the dynamics of cheap talk interactions between an oblivious receiver and sender with different amounts of information. Even though it may seem that having additional information about the state of the game is always beneficial to the sender, we show that there are cases in which garbling the information of a fully informed sender can improve not only receiver's utility in equilibrium, but also that of the sender herself. We also provide efficient algorithms that output the optimal amount of information in sender-receiver scenarios with binary actions and extend some of these results to settings with multiple senders and one receiver.

This paper considers the dynamics of cheap talk interactions between a sender and receiver, departing from conventional models by focusing on the receiver's perspective. We study two models, one with transparent motives and another one in which the receiver can \emph{filter} the information that is accessible by the sender. We give a geometric characterization of the best receiver equilibrium under transparent motives and prove that the receiver does not benefit from filtering information in this case. However, in general, we show that the receiver can strictly benefit from filtering and provide efficient algorithms for computing optimal equilibria. This innovative analysis aligns with user-based platforms where receivers (users) control information accessible to senders (sellers). Our findings provide insights into communication dynamics, leveling the sender's inherent advantage, and offering strategic interaction predictions.

Protocols for tossing a common coin play a key role in the vast majority of implementations of consensus. Even though the common coins in the literature are usually fair (they have equal chance of landing heads or tails), we focus on the problem of implementing a biased common coin such that the probability of landing heads is p ∈ [0, 1]. Even though biased common coins can be implemented using fair common coins, we show that this can require significant inter-party communication. In fact, we show that there is no bound on the number of messages needed to generate a common coin of bias p in a way that tolerates even one malicious agent, even if we restrict p to an arbitrary infinite subset of [0, 1] (e.g., {1/2n: n ∈ {0, 1, 2, …}}) and assume that the system is synchronous. By way of contrast, if we do not require the protocol to tolerate a faulty agent, we can do this. Thus, the cause of the message complexity is the requirement of fault tolerance.

We consider $k$-resilient sequential equilibria, strategy profiles where no player in a coalition of at most $k$ players believes that it can increase its utility by deviating, regardless of its local state. We prove that all $k$-resilient sequential equilibria that can be implemented with a trusted mediator can also be implemented without the mediator in a synchronous system of $n$ players if $n >3k$. In asynchronous systems, where there is no global notion of time and messages may take arbitrarily long to get to their recipient, we prove that a $k$-resilient sequential equilibrium with a mediator can be implemented without the mediator if $n > 4k$. These results match the lower bounds given by Abraham, Dolev, and Halpern (2008) and Geffner and Halpern (2023) for implementing a Nash equilibrium without a mediator (which are easily seen to apply to implementing a sequential equilibrium) and improve the results of Gerardi, who showed that, in the case that $k=1$, a sequential equilibrium can be implemented in synchronous systems if $n \ge 5$.

We study an information design problem with two informed senders and a receiver in which, in contrast to traditional Bayesian persuasion settings, senders do not have commitment power. In our setting, a trusted mediator/platform gathers data from the senders and recommends the receiver which action to play. We characterize the set of implementable action distributions that can be obtained in equilibrium, and provide an O(n log n) algorithm (where n is the number of states) that computes the optimal equilibrium for the senders. Additionally, we show that the optimal equilibrium for the receiver can be obtained by a simple revelation mechanism.

In this paper, we study an extension of the classic long cheap talk equilibrium introduced by Aumann and Hart~\citeN{aumann-hart-03}, and ask how much can the players benefit from having a trusted mediator compared with the standard unmediated model. We focus on a setting where a fully informed sender without commitment power must disclose its information to influence the behavior of a self-interested receiver. We show that, in the case of binary actions, even though a mediator does not help neither the sender nor the receiver directly, it may still allow improving the payoff of an external decision-maker whose utility is affected by the realized state and the receiver's action. Moreover, we show that if there are more than two actions, there exist games in which both the sender and the receiver simultaneously benefit from mediation.

Abraham, Dolev, Geffner, and Halpern [ 1 ] proved that, in asynchronous systems, a (k, t)-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4( k+t ), where an equilibrium is ( k, t )-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4( k+t ) there exist ( k, t )-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing ( k, t )-robust mediators seems closely related to implementing asynchronous multiparty ( k+t )-secure computation [ 6 ], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of ( k+t )-secure computation, which we call ( k+t )-strict secure computation , to implementing ( k, t )-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be ( k+t )-strictly securely computed if n ≤ 4( k+t ). This also provides a simple alternative proof for the well-known lower bound of 4 t +1 on asynchronous secure computation in the presence of up to t malicious agents [ 4 , 8 , 10 ].

In an information aggregation game, a set of senders interact with a receiver through a mediator. Each sender observes the state of the world and communicates a message to the mediator, who recommends an action to the receiver based on the messages received. The payoff of the senders and of the receiver depend on both the state of the world and the action selected by the receiver. This setting extends the celebrated cheap talk model in two aspects: there are many senders (as opposed to just one) and there is a mediator. From a practical perspective, this setting captures platforms in which strategic experts advice is aggregated in service of action recommendations to the user. We aim at finding an optimal mediator/platform that maximizes the users' welfare given highly resilient incentive compatibility requirements on the equilibrium selected: we want the platform to be incentive compatible for the receiver/user when selecting the recommended action, and we want it to be resilient against group deviations by the senders/experts. We provide highly positive answers to this challenge, manifested through efficient algorithms.

Nash equilibrium is often heralded as a guiding principle for rational decision-making in strategic interactions. However, it is well-known that Nash equilibrium sometimes fails as a reliable predictor of outcomes, with two of the most notable issues being the fact that it is not resilient to collusion and that there may be multiple Nash equilibria in a single game. In this paper, we show that a mechanism designer can get around these two issues for free by expanding the action sets of the original game. More precisely, given a normal-form or Bayesian game $\Gamma$ and a Nash equilibrium $\vec{\sigma}$ in $\Gamma$, a mechanism designer can construct a new game $\Gamma^{\vec{\sigma}}$ by expanding the action set of each player and defining appropriate utilities in the action profiles that were not already in the original game. We show that the designer can construct $\Gamma^{\vec{\sigma}}$ in such a way that (a) $\vec{\sigma}$ is a semi-strong Nash equilibrium of $\Gamma^{\vec{\sigma}}$, and (b) $\vec{\sigma}$ Pareto-dominates or quasi Pareto-dominates all other Nash equilibria of $\Gamma^{\vec{\sigma}}$.

A mediator can help non-cooperative agents obtain an equilibrium that may otherwise not be possible. We study the ability of players to obtain the same equilibrium without a mediator, using only cheap talk, that is, nonbinding pre-play communication. Previous work has considered this problem in a synchronous setting. Here we consider the effect of asynchrony on the problem, and provide upper bounds for implementing mediators. Considering asynchronous environments introduces new subtleties, including exactly what solution concept is most appropriate and determining what move is played if the cheap talk goes on forever. Different results are obtained depending on whether the move after such "infinite play" is under the control of the players or part of the description of the game.

Secure function computation has been thoroughly studied and optimized in the past decades. We extend techniques used for secure computation to simulate arbitrary protocols involving a mediator. The key feature of our notion of simulation is that it is bidirectional: not only does the simulation produce only outputs that could happen in the original protocol, but the simulation produces all such outputs. In asynchronous systems there are also new subtleties that arise because the scheduler can influence the output. Thus, these requirements cannot be achieved by the standard notion of secure computation. We provide a construction that is secure if \(n > 4t\), where t is the number of malicious agents, which is provably the best possible. We also show that our construction is secure in the universal composability model and that it satisfies additional security properties even if \(3t < n \le 4t\).

A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice paths. As a consequence of our results, we obtain an efficient scheme for encoding simple outerplanar maps.