Perfect Equilibrium Research Articles

Multi‐narrow type obstacle avoidance algorithm for UAV swarm based on game theory

AbstractA Flocking obstacle avoidance algorithm based on the extensive game with perfect information is proposed for the blockage problem of UAV swarm in front of multi‐narrow type obstacles. The two UAVs closest to the target are selected as participants of the game, and the game tree is defined to determine the combination of the motion strategies of the two UAVs to obtain the payoff matrix. Determine the subgame perfect Nash equilibrium to get the optimal strategy, and give the UAVs different motion states respectively so as to ensure that the UAVs can successfully pass multi‐narrow type obstacles. Simulation results demonstrate that the proposed algorithm has a higher over‐hole rate in the case of the multi‐narrow type obstacle compared to the static game‐based Flocking obstacle avoidance algorithm.

Impact of information disclosure on global supply chain greenwashing: Is more information transparency always better?

As supply chains become more globalized, retailers outsource the manufacturing of their products to foreign suppliers. Supply chain greenwashing is an immoral practice employed by retailers whereby they selectively disclose information regarding upstream suppliers after exaggerating the environmental benefits of their fake green products to consumers. Using a perfect Bayesian Nash equilibrium approach, this paper examines the conditions under which a retailer who engages in greenwashing will disclose the information of an unethical foreign supplier under pressure from enhanced scrutiny by a non-governmental organization (NGO). The results show that when the increase in the NGO’s utility from targeting the unrevealed upstream supplier is sufficiently large, the greenwashing retailer prefers to disclose the unethical foreign supplier’s information, whereas when the increased utility is low, the greenwashing retailer prefers to hide the unethical foreign supplier. Different from common belief that increased information transparency may be beneficial, we find that it does not necessarily lead to reduced social damage and that it depends on the unethical foreign supplier’s capability for compliance. In particular, when the unethical foreign supplier has a low capacity for compliance, the supply chain’s transparency advantage will lead to more fake green goods being sold, thus causing greater social damage.

Delay to Deal: Bargaining with Indivisibility and Round-Dependent Transfer

We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the initial transfer is large enough, the subgame perfect Nash equilibrium consists of a finite number of rounds of delay before an agreement is reached. The equilibrium delay is longer when the players are more patient, and when the transfer is initially higher and depreciates slower. Nevertheless, the game’s chaotic characteristic makes it arduous to forecast the exact number of delayed rounds or which player will make the ultimate decision. This game can be applied to many social scenarios, particularly those with exogenous costs.

A dynamic climate negotiation game achieving full cooperation

We present a repeated participation game where countries form a coalition for international environmental agreements over infinitely many periods. Countries may leave and re-enter coalitions. Payoff transfers are possible. In contrast to the literature on stable coalitions in a static model, we show that there exists a state-dependent subgame perfect equilibrium where the grand coalition forms in every period if countries are sufficiently patient. The grand coalition forms under countries' self-fulfilling belief that small coalitions will dissolve or enlarge to the grand coalition with an unfavorable transfer to non-participants. We further show that if coalitions are irreversible, the grand coalition gradually forms in finitely many periods in every Markov perfect equilibrium. The results are independent of a particular solution for the bargaining problem of coalition benefits.

Calculation of Perfect Bayesian Equilibrium in a Signaling Game

Calculation of Perfect Bayesian Equilibrium in a Signaling Game

Quantitative easing rules as a means to achieve optimal levels of structural reforms and government deficits in a monetary union

AbstractThis paper uses a tractable game theory model to study the interactions of structural reforms and fiscal and monetary policies in the European Monetary Union (EMU). Considering the externalities that arise when interest rates have hit the lower bound and monetary policy is carried out through quantitative easing (QE), we show that the subgame perfect equilibrium is suboptimal when structural reforms and fiscal policy are implemented at a national level. Then, we prove that the optimal outcome cannot be obtained if structural reforms are dictated by a supranational institution. By contrast, we establish that the first best can be obtained either by a full‐fledged fiscal union or a rule on QE. Given the practical difficulties that the first of these two solutions have encountered in the EMU, a rule over QE provides a clear, easier and more credible way to make structural reforms and fiscal deficits achieve the levels that maximise the union's welfare.

Losing money to make money: The benefits of redistribution in collective bargaining in sports

I develop a model of majority-rule collective bargaining between a sports league and its players when delay costs incurred by players are wealth-dependent. I propose a refinement of subgame perfect equilibrium that requires equilibrium strategies to be immune to deviations by any majority subgroup. I show this is equivalent to giving the player with median bargaining power the unilateral ability to negotiate with the league. Using this model, I demonstrate that policies reallocating surplus from high-talent to moderate-talent players, such as maximum contracts in professional sports, can improve the welfare of all players. Redistribution of surplus harmonizes players' interests, giving a majority of them a greater stake in the bargaining outcome. The model highlights the gains to be had if a heterogeneous group agrees to concessions that increase the alignment of their individual interests.

Accomplice plea bargains in the presence of costly juror effort

This is the first paper to study accomplice plea bargains when motivated jurors incur an effort cost. I find that a prosecutor who wishes to ensure punishment for the guilty, and acquittal for the innocent, induces a unique perfect Bayesian equilibrium which is fully separating, simultaneously minimizing court costs as well as jurors' cognitive efforts. In this equilibrium, a very harsh plea bargain (with negligible plea discounting) is offered, and is accepted by all guilty defendants, and rejected by all innocent ones. Though the prosecutor has the ability to induce semi-separating equilibria, he will prefer the fully separating one. We can use the Cho-Kreps intuitive criterion to show that a pooling equilibrium does not exist. My results contrast sharply with the plea bargaining literature which finds a tradeoff between sorting efficiency and the harshness of punishments meted out to the guilty and which does not support a fully separating equilibrium.

Strategic product compatibility in network industries

This article considers a product’s compatibility as a strategic variable in a Cournot duopoly with network consumption externalities. It develops a non-cooperative compatibility decision game (CDG) in which firms choose whether to let products be (in)compatible. With costless compatibility, the unique (Pareto-efficient) sub-game perfect Nash equilibrium (SPNE) of the CDG is universal compatibility. With quasi-fixed compatibility costs, the SPNE depends on whether product compatibility is an endogenous (i.e., a profit-maximising) or exogenous (i.e., given by technical constraints) variable. In the case of endogenous compatibility, the SPNE can vary from one unique to multiple regimes of (in)compatibility, such as the anti-prisoner’s dilemma (deadlock), prisoner’s dilemma, and coordination game. In the case of exogenous compatibility, the SPNE can become an anti-coordination game as well. The article also discusses the welfare outcomes corresponding to the SPNE.

Epistemic foundation of the backward induction paradox

After having observed a deviation from backward induction, a player might deem the opponent prone to deviate from backward induction again, making it worthwhile to deviate themself. Such reaction might make the deviation by the opponent worthwhile in the first place—which is the backward induction paradox. This argument against backward induction cannot be made in games where all players choose only once on each path. While strategic-form perfect equilibrium yields backward induction in games where players choose only once on each path but not necessarily otherwise, no existing non-equilibrium concept captures the backward induction paradox by having these properties. To provide such a concept, we define and epistemically characterize the concept of independently permissible strategies. Since beliefs are modeled by non-Archimedean probabilities, meaning that some opponent choices might be assigned subjective probability zero without being deemed subjectively impossible, special attention is paid to the formalization of stochastically independent beliefs.

Proportional resource allocation in dynamic [formula omitted]-player Blotto games

In this note, we introduce a general model of dynamic n-player multi-battle Blotto contests in which asymmetric resources and non-homogeneous battlefield prizes are possible. Each player’s probability of winning the prize in a battlefield is governed by a ratio-form contest success function and players’ resource allocation on that battlefield. We show that there exists a pure subgame perfect equilibrium in which players allocate their resources in proportion to the battlefield prizes for every history. We also give a sufficient condition that if there are two players and the contest success function is of Tullock type, then the subgame perfect equilibrium is unique.

Incentive compatibility in sender-receiver stopping games

We introduce a model of sender-receiver stopping games, in which the sender observes the current state, and sends a message to the receiver to either stop the game, or to continue. The receiver, only seeing the message, then decides to stop the game, or to continue. The payoff to each player is a function of the state when the receiver quits, with higher states leading to better payoffs.We prove existence and uniqueness of responsive Perfect Bayesian Equilibrium (PBE) when players are sufficiently patient. The responsive PBE has a simple structure, with a threshold strategy for the sender, and the receiver obediently following the recommendations of the sender. Hence, the sender alone plays the decisive role, and therefore always obtains the best possible payoff for himself.

Water Activity Prediction and Moisture Absorption Isotherms in Plant Food Preservation

The fraction of the water content in a meal (P) to the humidity of pure water is used to represent water activities (aw) (P0). It foretells if water would likely transfer from the packaged food into any potential microorganisms' cells. aw= P/P0. The difference in between vapour temperature of the meal when it is in perfect equilibrium with the air waves around it and the vapour pressure of distilled water in the same circumstances is the food's moisture activities (aw). SPSS statistics is a lithium chloride monohydrate, Potassium acetate, Magnesium nitrate hexahydrate, Sodium chloride, Cadmium Chloride, Potassium Chromate, Lithium sulfate, Sodium hydrogen phosphate, potassium sulfate. The Cronbach's Alpha Reliability result. The overall Cronbach's Alpha value for the model is 0.424 which Indicates 40 % reliability. From the literature review, the above 40% Cronbach's Alpha value model can be Considered for analysis. the outcome of Cronbach's alpha reliability Models is of total cranberry Alpha score is 0.424, which Denotes a 40% dependability level. The 40% Cronbach's Alpha value model mentioned above from the literature Review may be used for analysis.

Markov Decision Processes with Time-Varying Geometric Discounting

Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the necessity of modeling time-varying discounting in certain applications. This paper studies a model of infinite-horizon MDPs with time-varying discount factors. We take a game-theoretic perspective – whereby each time step is treated as an independent decision maker with their own (fixed) discount factor – and we study the subgame perfect equilibrium (SPE) of the resulting game as well as the related algorithmic problems. We present a constructive proof of the existence of an SPE and demonstrate the EXPTIME-hardness of computing an SPE. We also turn to the approximate notion of epsilon-SPE and show that an epsilon-SPE exists under milder assumptions. An algorithm is presented to compute an epsilon-SPE, of which an upper bound of the time complexity, as a function of the convergence property of the time-varying discount factor, is provided.

A participant selection based vehicle platoon asynchronous federated learning framework

AbstractIn the vehicular network, federated learning is an emerging paradigm to train deep learning models safely. However, the non‐identically independent distributed data collected by intelligent connected vehicles, expensive training overhead, and the existence of malicious participants significantly affect the efficiency of training and constrain the development of federated learning in the vehicular network. To address the above issues, this paper proposes a participant selection‐based asynchronous federated learning framework for an intelligent connected vehicle platoon. We proposed a platoon‐based asynchronous federated learning framework that effectively improves training efficiency through data share and asynchronous optimization. Also, We designed a signaling game‐based participant selection strategy that accurately identifies the potentially malicious participants by analyzing the Perfect Bayesian Equilibrium. The comparison experiment result shows the training model using our proposed scheme converges faster than the baseline scheme and gains approximately 10% higher accuracy.

Dynamic demand and noncompetitive intertemporal output adjustments: correction and extension

While hundreds of papers study the strategic interactions of oligopolists facing sticky prices only very few treat the in my opinion more important and opposite case of sticky or sluggish demand and supply, e.g., for energy. This point was taken up in Wirl (Int J Ind Organ 28:220–229, 2010) but unfortunately, the computation of the linear Markov perfect equilibrium is wrong. The situation in energy markets following Russia’s invasion of Ukraine adds a topical element to the theoretical analysis. Application to the oil market suggests that the difference between collusion and oligopolistic competition among few (symmetric) players is small for Markov perfect linear eqilibria. This is in stark contrast to the outcome in open loop strategies.

Research on supply chain pricing decisions considering the advertising effect under market encroachment

Based on a Stackelberg game, this paper establishes supply chain models in which an incumbent manufacturer invests in advertising and the retailer invests in advertising when there is a new entrant manufacturer. By solving the model, the subgame perfect equilibrium under different conditions is obtained, and then the influences of the advertising coefficient and the degree of differentiation of two brands on the pricing decisions of supply chain members are investigated. The results show that: in the incumbent manufacturer advertising model, the wholesale prices and retail prices of the incumbent manufacturer and the encroaching manufacturer change as the advertising coefficient and the degree of differentiation of the two brands change. In the retailer’s advertising model, the wholesale prices, retail prices and profits of the incumbent manufacturer and the encroaching manufacturer are all higher than those of the benchmark model within the limited scope. Some valuable information could be provided for supply chain enterprises to develop collaborative strategies and promote supply chain management practices.

A new value for cooperative games based on coalition size

AbstractWe propose and characterize a new value for TU cooperative games based on egalitarian distribution of worths in smaller coalitions and players' marginal productivity in larger coalitions. This value belongs to the class of Procedural values due to Malawski. Our value is identical with the Shapley value on one extreme and the Equal Division rule on the other extreme. We show that our value is identical with the solidarity value due to Bèal et al. of the dual game. However, by duality, our characterization intuitively improves over the axiomatization of this solidarity value. We also provide a mechanism that implements our value in sub‐game perfect Nash equilibrium. Finally, a generalized version of this value is proposed followed by its characterizations.

Liquid Crystal Assembly for Ultra-dissymmetric Circularly Polarized Luminescence and Beyond.

Circularly polarized luminescence (CPL) is attracting much interest because it can carry extensive optical information. CPL shows left- or right-handedness and can be regarded as part of high-level visual perception to supply an extra dimension of information with regard to regular light. A key to meeting the needs for practical applications is to develop the emerging field of ultra-dissymmetric CPL. Chiral liquid crystal (LC) assemblies─otherwise referred to as cholesteric liquid crystals (CLCs)─are essentially organized helical superstructures with a highly ordered one-dimensional orientation, and distinctly superior to regular helical supramolecules. CLCs can achieve a perfect equilibrium of molecular short-range interaction and long-range orientational order, enabling molecule-scale chirality on a helical pitch and observable scale. LC assembly could be an ideal strategy for amplifying chirality, making it accessible to ultra-dissymmetric CPL. Herein, we focused on some basic but important issues regarding CPL: (i) How can CPL be created from chiral dyes? (ii) Is the chirality of luminescent dyes an essential factor for the generation of CPL? That is, can all chiral dyes emit CPL and vice versa? (iii) How can CPL be transferred within intermolecular systems, and what principles of CPL transmission should be followed? Given these queries and our work, in this Perspective we discuss the generation, transmission, and modulation of CPL with chiral LC assembly, aiming to design and build up novel chiroptical materials. Recent applications of CPL-active LC microstructures in three-dimensional displays, circularly polarized lasers, and asymmetric catalysis are also discussed.

Divide and choose: An informationally robust strategic approach to bankruptcy problems

This paper proposes a simple and general strategic approach for analyzing bankruptcy problems. We construct three strategic bargaining games and show that they yield unique subgame perfect equilibrium (SPE) outcomes that coincide with the allocations given by the three prominent solution concepts, the constrained equal awards rule, the constrained equal losses rule and the Talmud rule, respectively. We also discuss the robustness of the result in the presence of certain incomplete information. The approach can be readily extended to study alternative solutions for bankruptcy problems or other settings such as surplus sharing problems, and is further enriched by considering a voting stage. Central to all these bargaining protocols is an extended and context-fitting “divide-and-choose” mechanism.