Dominant Strategy Equilibrium Research Articles

A Nash equilibrium against gun control

This work constructs a non-cooperative, static game of gun control between the citizen and a pacifistic society characterised by law enforcement imperfection, by which the retention of firearms and the certitude of punishment against all crimes emerge both as a strict Nash equilibrium, in pure strategies, and as a strict dominant strategy equilibrium. The reason is that ratified by the Second Amendment to the American Constitution, discerning the necessity of a militia to the individual and societal security of a free state, by which the right of the people to keep and bear arms cannot be infringed.

Symmetric mechanism design: Comment

In an earlier paper published in this journal, Azrieli and Jain (2018) claim that a social choice function (SCF) is symmetrically implementable in a dominant strategy equilibrium only if the SCF is symmetric. This result crucially relies on their notion of dominant strategy, which is used in the game theory literature and is stronger than the one traditionally used in the mechanism design literature. We discuss the limitation of using their notion in mechanism design and provide a set of characterizations of symmetric mechanism design using the (weaker) standard notion that differ from their findings.

Reward Poisoning Attacks on Offline Multi-Agent Reinforcement Learning

In offline multi-agent reinforcement learning (MARL), agents estimate policies from a given dataset. We study reward-poisoning attacks in this setting where an exogenous attacker modifies the rewards in the dataset before the agents see the dataset. The attacker wants to guide each agent into a nefarious target policy while minimizing the Lp norm of the reward modification. Unlike attacks on single-agent RL, we show that the attacker can install the target policy as a Markov Perfect Dominant Strategy Equilibrium (MPDSE), which rational agents are guaranteed to follow. This attack can be significantly cheaper than separate single-agent attacks. We show that the attack works on various MARL agents including uncertainty-aware learners, and we exhibit linear programs to efficiently solve the attack problem. We also study the relationship between the structure of the datasets and the minimal attack cost. Our work paves the way for studying defense in offline MARL.

Optimal Procurement with Quality Concerns

Adverse selection in procurement arises when low-cost bidders are also low-quality suppliers. We propose a mechanism called LoLA (lowball lottery auction) which, under some conditions, maximizes any combination of buyer’s and social surplus, subject to incentive compatibility, in the presence of adverse selection. The LoLA features a floor price, and a reserve price. The LoLA has a dominant strategy equilibrium that, under mild conditions, is unique. In a counterfactual analysis of Italian government auctions, we compute the gain that the government could have made, had it used the optimal procurement mechanism (a LoLA), relative to a first-price auction (the adopted format). (JEL D44, D82, H57, L14)

The economics of China’s between-city height competition: A regression discontinuity approach

In this article, I use a regression discontinuity design to quantify the race between Chinese cities to build taller skyscrapers. I begin by characterizing this height competition with a game-theoretic model for multi-stage, two-player, all-pay auctions with carryover. The dominant mixed strategy equilibrium of this dynamic game implies that a city would be more inclined to construct a taller skyscraper if its current tallest building is merely shorter than the tallest in the rival city, and this inclination is discontinuous at which the heights of these two buildings are equal. Utilizing a large data set of China’s skyscrapers constructed between 2004 and 2019, I confirm the presence of this between-city contest by empirically identifying the discontinuity in a city’s probability of constructing a taller building. I also find that this height competition has been more prevalent among the cities with fewer historic amenities or with leaders that have lower promotion likelihoods prior to the start of office.

When does an additional stage improve welfare in centralized assignment?

We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools’ capacity-priority profiles under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage system to the truthful dominant-strategy equilibrium outcome of the 1-stage system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage system may Pareto dominate the truthful dominant-strategy equilibrium outcome of the 1-stage system. If students are restricted to playing truncation strategies, an additional stage unambiguously improves student welfare: no student prefers the truthful dominant-strategy equilibrium outcome of the 1-stage system to any SPNE outcome of the 2-stage system.

Informationally Simple Incentives

We consider a mechanism design setting in which agents can acquire costly information on their preferences as well as others’. A mechanism is informationally simple if agents have no incentive to learn about others’ preferences. This property is of interest for two reasons. First, it is a necessary condition for the existence of dominant-strategy equilibria in the extended game. Second, this endogenizes an “independent-private-value” property of the interim information structure. We show that, generically, a mechanism is informationally simple if and only if it satisfies a separability condition that rules out most economically meaningful mechanisms.

Incompatibility of Laws and Natural Resources: A Case Study of Land Revenue Laws and Their Implications in Federal Areas of Pakistan

Better rule of law would generate economic growth, which would in turn build constituencies for democratic reforms [Root and May (2006)]. Consider prisoners dilemma, to Law and Economics Scholars, the inevitability of prisoner’s dilemmas arising to block potentially efficient exchanges explains the need for and consequently the adoption of contract law. When the law enforces contracts, it permits the participants in a potential prisoners’ dilemma the option of escaping the dominant strategy equilibrium of non-cooperation, which prevents the achievement of efficient exchanges, by permitting the parties to effectively pre-commit to future cooperative behavior. Mutual pre-commitments can produce the efficient cooperate-cooperate equilibrium. The existence of contract law then tends to foster efficient cooperative behaviour. Institutions are considered to provide the mechanisms by which individuals can resolve social dilemmas [Steins (1999)]. They are sets of rules that people have created in order to control/regulate the behavior of people using a natural resource. Several layers of institutions are important for institutional development and economic performance. These layers, from the slowest moving to the fastest moving are: human motivations and social institutions, political institutions, legal institutions and private institutions [Azfar (2006)]. Institutions perform their role to frame rules, procedure and enabling environment for implementation of rules. Rights of individuals are recognised and recognised through institutions as well.

Double Implementation in Dominant Strategy Equilibria and Ex-Post Equilibria with Private Values

Abstract We consider the implementation problem for incomplete information and private values. We investigate double implementability of social choice functions in dominant strategy equilibria and ex-post equilibria. We define a new strategic axiom that implies “strategy-proofness” and that is implied by “secure strategy-proofness,” but the converse of these relationships does not hold. We call it “weak secure-strategy-proofness.” We show that a social choice function is doubly implementable if and only if it is weakly securely-strategy-proof.

An auction mechanism for platoon leader determination in single-brand cooperative vehicle platooning

Cooperative vehicle platooning enabled by connected automated vehicle (CAV) technology has been identified to bring energy savings and driving-effort reduction. However, the intrinsic difference of gained benefits between the leading vehicle and the following vehicles hampers the spontaneous platooning via peer-to-peer coordination. This study proposes an auction mechanism that determines the leader–follower positioning together with the associated benefits, for facilitating the formation and maintaining the behavioral stability of vehicle platoons in a distributed way. We theoretically prove that there is no mechanism to achieve an efficient outcome in an ex post equilibrium, requiring individual rationality and budget balance. In this regard, we provide a truthful ε-approximate auction mechanism that deploys a linear transfer function, which guarantees that the implemented outcome is an efficient approximate dominant strategy equilibrium.

A dominant strategy double clock auction with estimation‐based tâtonnement

The price mechanism is fundamental to economics but difficult to reconcile with incentive compatibility and individual rationality. We introduce a double clock auction for a homogeneous good market with multidimensional private information and multiunit traders that is deficit‐free, ex post individually rational, constrained efficient, and makes sincere bidding a dominant strategy equilibrium. Under a weak dependence and an identifiability condition, our double clock auction is also asymptotically efficient. Asymptotic efficiency is achieved by estimating demand and supply using information from the bids of traders that have dropped out and following a tâtonnement process that adjusts the clock prices based on the estimates.

Incentive Compatible Cost Sharing of a Coalition Initiative with Probabilistic Inspection and Penalties for Misrepresentation

This research proposes cost sharing mechanisms such that payments for a coalition initiative are allocated among players based on their honest valuations of the initiative, probabilistic inspection efforts, and deception penalties. Specifically, we develop a set of multiobjective, nonlinear optimization problem formulations that alternatively impose Bayesian incentive compatible, strategyproof, or group strategyproof mechanisms with generalized cost sharing and penalty functions that can be tailored to specific applications. Any feasible solution to these problems corresponds to a Bayesian game with stochastic payoffs wherein a collectively honest declaration is a Bayes–Nash equilibrium, a Nash equilibrium in dominant strategies, or a collusion resistant Nash equilibrium, respectively, and wherein an optimal solution considers the central authority’s relative priorities between inspection and penalization. In addition to this general framework, we introduce special cases having specific cost sharing and penalty functions such that the set of mechanisms are budget-balanced-in-equilibrium and proportional by design. The convexity of the resulting mathematical programs are examined, and formulation size reductions due to constraint redundancy analyses are presented. The Pareto fronts associated with each multiobjective optimization problem are assessed, as are computer memory limitations. Finally, an experiment considers the clustering of available valuations and the player probability distributions over them to examine their effects.

Strategy-proofness in experimental matching markets

We introduce two novel matching mechanisms, Reverse Top Trading Cycles (RTTC) and Reverse Deferred Acceptance (RDA), with the purpose of challenging the idea that the theoretical property of strategy-proofness induces high rates of truth-telling in economic experiments. RTTC and RDA are identical to the celebrated Top Trading Cycles (TTC) and Deferred Acceptance (DA) mechanisms, respectively, in all their theoretical properties except that their dominant-strategy equilibrium is to report one’s preferences in the order opposite to the way they were induced. With the focal truth-telling strategy being out of equilibrium, we are able to perform a clear measurement of how much of the truth-telling reported for strategy-proof mechanisms is compatible with rational behaviour and how much of it is caused by confused decision-makers following a default, focal strategy without understanding the structure of the game. In a school-allocation setting, we find that roughly half of the observed truth-telling under TTC and DA is the result of naive (non-strategic) behaviour. Only 14–31% of the participants choose actions in RTTC and RDA that are compatible with rational behaviour. Furthermore, by looking at the responses of those seemingly rational participants in control tasks, it becomes clear that most lack a basic understanding of the incentives of the game. We argue that the use of a default option, confusion and other behavioural biases account for the vast majority of truthful play in both TTC and DA in laboratory experiments.

Auctions with quantity externalities and endogenous supply

This paper studies the design of license auctions when the number of licenses allocated in the auction determines structure of the post-auction market. I first show that a sequence of conditional reserve prices that specify minimum acceptable bid at each supply level can be used to determine supply endogenously. Then I construct a static auction called multi-dimensional uniform-price auction and a dynamic auction called Walrasian clock auction that allow the auctioneer to condition reserve price on supply and allow bidders to condition bids on supply. I show that both proposed auctions can implement the efficient market structure that maximizes total surplus in the post-auction market in a dominant strategy equilibrium. I next characterize the optimal auction and show that the two proposed auctions can yield the optimal revenue under a sequence of optimal reserve prices.

Strategy-Proof Mechanism Design with Boundedly Rational Agents

This paper considers an implementation problem with bounded rationality of the agents. Bounded rationality presented here means that the agent might choose the agent's best response which is different from the agent's dominant strategy. To describe such a behavior, this paper introduces a new notion of equilibrium, called (n-k)-dominant strategy Nash equilibrium, in which at most k∈{0,1,⋯,n} boundedly rational agents might choose their best responses which are different from their dominant strategies and at least (n-k) rational agents choose their dominant strategies. In addition, to show what a socially optimal outcome collectively chosen under the existence of boundedly rational agents, this paper introduces a new notion of implementation, called k-secure implementation, which is double implementation in dominant strategy equilibria and (n-k)-dominant strategy Nash equilibria. In specific environments with k≤(n+1)/2, this paper shows that majority rule and the median voter rule satisfy k-secure implementability, but not secure implementability (Saijo, T., T. Sjostrom, and T. Yamato (2007) “Secure Implementation,” Theoretical Economics 2, pp.203-229) which is equivalent to n-secure implementability respectively.

Informationally Simple Implementation

We consider a mechanism design setting in which agents can acquire costly information on their preferences as well as others’. The choice of the mechanism generates informational incentives as it affects what information is acquired before play begins. A mechanism is informationally simple if agents have no incentive to learn about others’ preferences. This property is of interest for two reasons: First, the extended game has an equilibrium in dominant strategies only if it is informationally simple. Second, this endogenizes an independent private value property of the interim information structure. Our main result is that a mechanism is informationally simple only if it is de facto dictatorial. This holds for generic environments and any smooth cost function which satisfies an Inada condition. Hence even interim strategy-proof mechanisms incentivize agents to learn about others, and do not admit dominant strategies at the ex-ante stage. Moreover, the Independent Private Value assumption is unlikely to arise endogenously, though we show that full surplus extraction is infeasible.

On the uniqueness of Nash equilibrium in strategic-form games

We consider a sufficient condition for the uniqueness of a Nash equilibrium in strategic-form games: for any two distinct strategy profiles, there is a player who can obtain a higher payoff by unilaterally changing the strategy from one strategy profile to the other strategy profile. An example of a game that satisfies this condition is the prisoner's dilemma. Viewed as a solution concept, the Nash equilibrium satisfying the condition is stronger than strict Nash Equilibrium and weaker than strict dominant strategy equilibrium.

An Auction Mechanism for Platoon Leader Determination in Single-Brand Cooperative Vehicle Platooning

Cooperative vehicle platooning enabled by connected automated vehicle (CAV) technology has been identified to bring energy savings and driving-effort reduction. However, the intrinsic difference of gained benefits between the leading vehicle and the following vehicles hampers the spontaneous platooning via peer-to-peer coordination. This study proposes an auction mechanism that determines the leader-follower positioning together with the associated benefits, for facilitating the formation and maintaining the behavioral stability of vehicle platoons in a distributed way. We theoretically prove that there is no mechanism to achieve an efficient outcome in an ex post equilibrium, requiring individual rationality and budget balance. In this regard, we provide a truthful $\epsilon-$approximate auction mechanism that deploys a linear transfer function, which guarantees that the implemented outcome is an efficient approximate dominant strategy equilibrium.

Trusted UAV Network Coverage Using Blockchain, Machine Learning, and Auction Mechanisms

The UAV is emerging as one of the greatest technology developments for rapid network coverage provisioning at affordable cost. The aim of this paper is to outsource network coverage of a specific area according to a desired quality of service requirement and to enable various entities in the network to have intelligence to make autonomous decisions using blockchain and auction mechanisms. In this regard, by considering a multiple-UAV network where each UAV is associated to its own controlling operator, this paper addresses two major challenges: the selection of the UAV for the desired quality of network coverage and the development of a distributed and autonomous real-time monitoring framework for the enforcement of service level agreement (SLA). For a suitable UAV selection, we employ a reputation-based auction mechanism to model the interaction between the business agent who is interested in outsourcing the network coverage and the UAV operators serving in closeby areas. In addition, theoretical analysis is performed to show that the proposed auction mechanism attains a dominant strategy equilibrium. For the SLA enforcement and trust model, we propose a permissioned blockchain architecture considering Support Vector Machine (SVM) for real-time autonomous and distributed monitoring of UAV service. In particular, smart contract features of the blockchain are invoked for enforcing the SLA terms of payment and penalty, and for quantifying the UAV service reputation. Simulation results confirm the accuracy of theoretical analysis and efficacy of the proposed model.

A Multi-PR Heuristic for Distributed Multi-Project Scheduling With Uncertain Duration

Multiple projects are often managed and run in a decentralized setting. In this paper, considering the uncertainty in project implementation, we study the distributed multi-project scheduling problem with uncertain duration. A multi-PR heuristic (MPR-H) is then proposed to dynamically coordinate the global resource conflicts while minimizing the expected total tardiness cost. Three priority rules based on current known information are also proposed and incorporated in our approach. We further consider the opportunistic behaviour of self-interested agents and design a payment negotiation process which is added to the MPR-H. In this paper, we then evaluate the performance of the MPR-H on the benchmark dataset MPSPLIB. The computational results confirm that MPR-H achieves significant improvements in comparison with several state-of-the-art distributed/centralized algorithms. The proposed algorithm also provides the senior manager with an efficient method to allocate global resources for large-size and strong conflicting instances under various activity duration distributions. Besides, we show that multi-projects with relative slack global resource constraints are more affected by the change of uncertainty. By analyzing the strategic behaviour of the agents in problems with two projects, we also show that in our MPR-H with payment negotiation approach, rational agents have to behave truthfully that is the dominant-strategy equilibrium leading to high-quality results.