Nash Bargaining Solution Research Articles

Realizing Synthetic Active Inference Agents, Part II: Variational Message Updates.

The free energy principle (FEP) describes (biological) agents as minimizing a variational free energy (FE) with respect to a generative model of their environment. Active inference (AIF) is a corollary of the FEP that describes how agents explore and exploit their environment by minimizing an expected FE objective. In two related papers, we describe a scalable, epistemic approach to synthetic AIF by message passing on free-form Forney-style factor graphs (FFGs). A companion paper (part I of this article; Koudahl etal., 2023) introduces a constrained FFG (CFFG) notation that visually represents (generalized) FE objectives for AIF. This article (part II) derives message-passing algorithms that minimize (generalized) FE objectives on a CFFG by variational calculus. A comparison between simulated Bethe and generalized FE agents illustrates how the message-passing approach to synthetic AIF induces epistemic behavior on a T-maze navigation task. Extension of the T-maze simulation to learning goal statistics and a multiagent bargaining setting illustrate how this approach encourages reuse of nodes and updates in alternative settings. With a full message-passing account of synthetic AIF agents, it becomes possible to derive and reuse message updates across models and move closer to industrial applications of synthetic AIF.

The Nash bargaining solution and utilitarian–egalitarian social welfare functions

The 2-person Nash bargaining solution is the only scale covariant one that maximizes, on every problem, some mixture of the utilitarian and egalitarian social welfare functions. With three or more players, no solution satisfies these two axioms.

The interface between authoritarian innovations and labour: Implications for the Indian workforce

On assuming office in 2014, India's BJP-led government initiated an ambitious plan to facilitate the ease of doing business, aiming to make India an attractive investment destination. Interview data from 20 trade union leaders and an expert and published data from ILO, government and trade union documents and newspaper archives reveal that, to advance this neoliberal agenda, the government did not use direct and obvious repressive tactics as was the case during the 1976 Emergency, but rather, a combination of discourse, manipulation of democratic institutions like the Parliament and a strategy for disengaging and disempowering the unions that oppose reforms. The new Labour Codes provide a facade for tackling the perennial problem of union recognition and collective bargaining that has plagued Indian industrial relations, but in their implementation, these Codes are likely to weaken unions and erode working conditions. The government's practices attempt to obscure precariousness and silence civil society organisations by imposing unprecedented restrictions on them and disengaging with them. Today, more than ever before, employment in India tends towards informality. Rather than strengthening unions, the government has created fissures in the labour movement by using the unions affiliated with it to manufacture a democratic debate on various pertinent issues, like the Labour Codes.

Resolving bargaining problems in civil conflicts: Goals, institutions and negotiations

Moderate (or ‘limited’) rebel goals and inclusive political institutions have been suggested to increase the chances of rebel–government negotiations. This article attempts to shed light on the politics of rebel–government negotiations by presenting new, systematic data on the scope of rebel goals and demonstrating both theoretically and empirically that it is the interaction of moderate rebel goals and inclusive political institutions – rather than each variable in isolation – that helps disputants overcome bargaining problems and engage in negotiations. Particularly, the article contends that while moderate rebel goals allow the disputants to recognize that negotiations may be mutually beneficial, the presence of a dual commitment problem – where rebel groups and governments are both concerned about the opponent’s commitment to negotiated settlements – hinders them from negotiating. In such cases, the institutional features of polyarchy, defined by Dahl as competitive and inclusive elections accompanied by civil liberties, alleviate this dual commitment problem and induce moderate rebels and the government to follow through with their incentives to negotiate. Statistical results from newly collected data on rebel group goals and rebel–government negotiations support this claim: rebel–government negotiations are significantly more likely to occur when rebel groups espouse moderate goals and the level of polyarchy in a country is sufficiently high. Results indicate that the influence of rebel goals and institutions on negotiations is better understood in conjunction.

Double‐edged stars: Michelin stars, reactivity, and restaurant exits in New York City

AbstractResearch SummaryThis article develops a theoretical framework to explicate how third parties, who are not transactionally involved in a given exchange relationship, can promote or impede the creation and capture of value by influencing market actor beliefs and behaviors. I investigate these issues empirically through an abductive mixed‐method case study of the Michelin Guide's entry into New York City. An examination of two decades of the openings and closings of New York City's elite restaurants indicates that receiving a Michelin star corresponded to an increased likelihood of restaurant exit. Michelin stars appear to have fostered disruptions at recipients' upstream and downstream interfaces, which inhibited their ability to capture value. This ultimately underscores how value network reactivity to third‐party evaluations may lead to unintended consequences for firms.Managerial SummaryThis article explains how third‐party evaluators' reviews, ratings, and rankings can promote or impede the creation and capture of value. This occurs because third‐party evaluations engender reactions by those being evaluated, as well as reactions by other market actors such as competitors and exchange partners. I study these issues within the context of the Michelin Guide's entry into New York City, and my findings indicate that restaurants that received a Michelin star were more likely to close in subsequent years. Evidence suggests that intensified bargaining problems with landlords, suppliers, and employees, along with heightened consumer expectations, created new challenges for these Michelin‐starred restaurants, which ultimately made it more difficult for them to stay in business.

A two-sided equilibrium model of Vehicle-to-Vehicle charging platform

A novel mobile charging service utilizing vehicle-to-vehicle (V2V) charging technology has been proposed as a complement to fixed charging infrastructure (CI), enabling electric vehicles (EVs) to exchange electricity. This study develops a two-sided equilibrium model for a V2V charging platform, where the demand-side charging vehicles (CVs) choose between charging piles and the V2V platform, and the supple-side discharging vehicles (DVs) decide whether to provide discharging services. The V2V platform matches CVs with DVs, receiving compensation from CV owners and reimbursing DV owners. To explore the strategic interactions between the V2V platform and fixed CI operators, we construct an analytical bi-level model that examines different operation regimes, including competitive and cooperative scenarios, i.e., non-cooperative game and Nash Bargaining game. The lower-level model is a two-sided equilibrium model that quantifies charging and discharging choices of EV owners, while the upper-level model optimizes the pricing decisions of the V2V platform and fixed CI operator. Numerical results indicate that the introduction of the V2V platform can reduce the overall charging costs, thus encourage the use of public charging services. Furthermore, it is suggested that the V2V platform be managed by independent enterprises, rather than existing fixed CI operators, to promote the EVs at relatively low charging costs.

Fair integer programming under dichotomous and cardinal preferences

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). We also discuss in detail how to extend the proposed methods when agents have cardinal preferences. As such, we embed the “black-box” procedure of solving an integer linear program into a framework that is explainable from start to finish. Lastly, we evaluate the proposed methods on two specific applications, namely kidney exchange (dichotomous preferences), and the scheduling problem of minimizing total tardiness on a single machine (cardinal preferences). We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

Nash Smoothing on the Test Bench: Hα-Essential Equilibria

Nash’s [1953] demand game models the second step in a “two-move game” that formalizes his “Negotiation Model”. Nash claimed for any two-person bargaining game [Formula: see text] the existence of a unique stable equilibrium of its associated second move demand game that by its payoff vector supports the symmetric Nash solution of that bargaining game. Nash’s negotiation game is considered the first contribution to the Nash program. Only weaker versions of stability than that claimed by Nash have been formally proven later by other authors. However, Nash’s request for “studying the relative stabilities” of the demand game’s equilibria has never been complied with. By performing that task, we establish analogous stability results for all generalized Nash solutions and thereby disprove Nash’s “unique stability” claim. Furthermore, we explain the impact of our result on the Nash solution with endogenous variable threats (NBWT) of the two move negotiation game, which is defined as the symmetric Nash solution of that bargaining game [Formula: see text] whose status quo point [Formula: see text] is the unique payoff vector of the payoff-equivalent equilibria of the first move threat game.

Step-by-step negotiations and the Nash bargaining solution: Efficiency-free characterizations

Real-world bargainings often proceed step-by-step: the agents make intermediate agreements today and continue to negotiate tomorrow to reach a final agreement. We consider two natural properties of the bargaining solutions in such step-by-step negotiations and show that the Nash solution is the only solution that satisfies either of them, a very weak axiom of individual rationality, and Nash’s axioms except for Pareto optimality.

Design optimization of offshore wind farm layout based on game theory

In offshore wind farm (OWF) planning, traditional methods usually use global optimal strategies. In this paper, game theory is applied to the multi-objective optimization of wind turbine (WT) micro-siting and cabling in an OWF. This method considers the real situation where two different teams may choose the global optimal or the local optimal solution. Firstly, the wind speed deficit in the OWF is estimated using the Gaussian wake model. The objective function and constraints of this optimization problem are formulated. Secondly, the game strategies are exhaustively enumerated. The strategies are allocated to the game space matrix and the payoffs are calculated. The above steps are repeated after redistributing the design permissions. Finally, the Nash front is formed and compared with the Pareto optimum. From simulation results, it can be observed that different Nash solutions can be obtained using different strategy permission allocation methods. So the final layout of the OWF should be determined according to different strategy allocation methods when planning the OWF.

Strategic selection between technology spillover and green technology cross-licencing under cap-and-trade policy

ABSTRACT This paper examines the co-opetition strategic selection between two rival manufacturers under a cap-and-trade policy. Based on the classical Cournot game and Nash bargaining game theories, we propose a benchmark model with technology spillover effect and green technology cross-licencing models with both fixed-fee and mixed-fee modes. The results show that manufacturers have the highest outputs in the fixed-fee cross-licencing scenario, and manufacturers’ total profits in the green technology cross-licencing scenarios always outperform that in the technology spillover scenario. Moreover, when the unit carbon quota trading price is high, the technology spillover scenario has the lowest emissions. When the unit cost of governing carbon emissions-related pollution is low, social welfare in the fixed-fee cross-licencing scenario is higher than that in the mixed-fee cross-licencing scenario. Interestingly, the social welfare advantage of the mixed-fee cross-licencing scenario becomes more and more prominent as the unit cost in governing carbon emissions related pollution increases.

Efficient demand management for the on-time arrival problem: A convexified multi-objective approach assuming macroscopic traffic dynamics

This work proposes a novel solution approach to address the On-Time Arrival (OTA) problem, considering macroscopic traffic dynamics. In this context, all drivers who intend to use the road infrastructure are required to communicate their origin–destination pair and desired arrival time to a central scheduler prior to starting their trip. In response, the scheduler assigns a departure time and a multi-regional route to each driver to make possible their on-time arrival at the destination. The OTA problem is formulated as a nonconvex, nonlinear, multi-objective optimization problem considering two objective criteria. The first criterion aims at minimizing the travel time of all drivers in the network to prevent congestion, while the second criterion seeks to minimize the discrepancy between the desired and actual arrival time. The proposed formulation is solved efficiently through an approximated convex solution that leverages the Normal Boundary Intersection (NBI) method to efficiently generate a representative sample of the Pareto Front. Additionally, two solution methodologies based on “knee” solution and the Nash Bargaining Game is proposed which can be used to select a unique solution across all the Pareto points, that offers a reasonable trade-off between the two objective criteria. Finally, simulation results demonstrate that the proposed solution can significantly reduce congestion while ensuring that most drivers will arrive at their destination on their desired time.

SPLITTING THE DIFFERENCE IN INCOMPLETE‐INFORMATION BARGAINING: THEORY AND WIDESPREAD EVIDENCE FROM THE FIELD

AbstractThis article documents a robust pattern from diverse sequential bargaining settings: agents favor offers that split the difference between the previous two offers. Our empirical settings include used cars, insurance claims, home sale, trade tariffs, a TV game show, eBay, and auto‐rickshaws. These even‐split offers are more likely to be accepted, less likely to spur exit by the opponent, and more likely to be followed by subsequent split‐the‐difference offers if bargaining continues. We propose several theoretical frameworks to explain this behavior, including an inference argument under which split‐the‐difference offers can be viewed as an equal split of the potential surplus.

Sum-rate maximization for a distributed space-time block code-aided cooperative NOMA with energy harvesting

AbstractIn this paper, we exploit the spatial and transmission diversities in cooperative non-orthogonal multiple access (C-NOMA) networks to improve the system sum-rate. To achieve this, we propose a user-pairing scheme where near-field user pairs serve as relays for user pairs in the far-field region. Based on this pairing scheme, we incorporate a space-time block code transmission technique at the near-field user pairs to maximize the transmission diversity in the cooperative phase. Moreover, we consider a non-linear energy harvesting model at the near-field user pair to alleviate the problem of energy consumption during the cooperative transmission phase. Further to this, we formulate a sum-rate maximization problem that is addressed from the viewpoint of joint power allocation factor and power splitting ratio optimization. We develop a low-computational iterative algorithm based on the concepts of the Stackelberg game and the Nash bargaining solution. We benchmark our findings with different scenarios, such as energy harvesting C-NOMA with a fixed power allocation factor and power splitting ratio, energy harvesting C-NOMA without STBC, non-cooperative NOMA, and orthogonal multiple access. The results obtained via simulations outperform the benchmark schemes.

Integrating Raiffa and Nash approaches to bargaining using interim agreements

Raiffa's solution to the bargaining problem, outlined in Luce and Raiffa (1957), is the point where the negotiation curve - a sequence of points that constitute step-by-step improvements from the status quo in the feasible payoff space - meets (possibly in the limit) the efficient boundary of the feasible region. A bargaining model with interim agreements yields a negotiation curve in equilibrium (in the spirit of Raiffa), and as the bargaining frictions disappear, the Raiffa path of payoffs converges to the Nash solution.

Evolutionary dynamic of division of labor games

The ubiquity of labor division within diverse social collectives is a topic well captured by evolutionary game theory. This work offers an integrative review of the evolutionary dynamics underpinning such division of labor from a tripartite standpoint —commencing with a theoretical exposition on numerous archetypes of labor division games. Subsequently, we delineate a suite of control strategies formulated to not only realize but also sustain the phenomenon of division of labor. This is followed by an elucidation of practical implementations pertaining to the allocation of tasks and labor division, grounded in the principles of game theory. We culminate with the proposition of prospective avenues and insightful trajectories for future investigations, cultivating a frontier for the continued exploration within this field.

Bargaining with Voluntary Disclosure and Endogenous Matching

We investigate a bargaining setting between an “informed” player, who has private information, and an “uninformed” player. The informed player has the option to truthfully disclose private information in two unique environments. In the first environment, the informed player is randomly matched with an uninformed player and, after matching, can voluntarily disclose private information prior to a negotiation taking place. In the second environment, the informed player can voluntarily disclose private information before any endogenous matching between players (and subsequent negotiation) takes place. We begin by examining these environments theoretically. When disclosure occurs after matching, we show that low informed types should disclose more often than high informed types to avoid disagreement. However, when disclosure occurs before matching, for a range of parameter values, we show that high informed types should disclose more than low informed types to secure a better match. We test these predictions in a controlled human-subjects experiment and verify many of the theoretical predictions. Among other results, we find that low informed types do indeed disclose their private information to avoid disagreement and that, when it is in their interest to do so, high informed types disclose their private information to secure a better match. Another key insight is that high uninformed types benefit from disclosure regardless of whether it occurs before or after matching. This paper was accepted by Axel Ockenfels, behavioral economics and decision analysis. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.03566 .

Two-Person Fair Division with Additive Valuations

In the literature, many desirable properties for allocations of indivisible goods have been proposed, including envy-freeness, Pareto optimality, and maximization of either the total welfare of all agents, the welfare of the worst-off agent, or the Nash product of agents’ welfares. In the two-person context, we study relationships among these properties using both analytical models and simulation in a setting where individual preferences are given by additive cardinal utilities. We provide several new theorems linking these criteria and use simulation to study how their values are related to problem characteristics, assuming that utilities are assigned randomly. We draw some conclusions concerning the relation of problem characteristics to the availabilty of allocations with particular properties.

Modeling Dynamic Bargaining and Stability in a Star-Shaped Trans-Shipment Network

The star-shaped trans-shipment network causes the retailer’s bargaining power to be different, which leads to the misalignment of trans-shipment profit. Aimed at this, we take retailers and the trans-shipment paths as the nodes and edges of the trans-shipment network. Based on this, we model the multilateral negotiations between the central retailer and the local retailer and adopt the Generalized Nash Bargaining game to derive the optimal solution of the value function for the incomplete trans-shipment network under the bargaining mechanism. Furthermore, we reveal the convexity of the optimal trans-shipment value function and give the condition that the allocation of the bargaining mechanism is in the core. Based on this, we introduce the concept of pairwise Nash equilibrium and show the star-shaped trans-shipment network is the optimal endogenous formation of the trans-shipment network. In practice, the central retailer should introduce as many local retailers as possible to join this trans-shipment alliance, which will achieve Pareto improvement. Meanwhile, the central retailer should order as many as possible. Finally, it is more appropriate to establish a star-shaped trans-shipment network when one retailer has stronger negotiation power compared to other retailers in a distribution system, which not only ensures the stability of the allocation of trans-shipment profits but also the stability of the trans-shipment network.

Fair Exploration via Axiomatic Bargaining

Exploration is often necessary in online learning to maximize long-term rewards, but it comes at the cost of short-term “regret.” We study how this cost of exploration is shared across multiple groups. For example, in a clinical trial setting, patients who are assigned a suboptimal treatment effectively incur the cost of exploration. When patients are associated with natural groups on the basis of, say, race or age, it is natural to ask whether the cost of exploration borne by any single group is “fair.” So motivated, we introduce the “grouped” bandit model. We leverage the theory of axiomatic bargaining, and the Nash bargaining solution in particular, to formalize what might constitute a fair division of the cost of exploration across groups. On one hand, we show that any regret-optimal policy strikingly results in the least fair outcome: such policies will perversely leverage the most “disadvantaged” groups when they can. More constructively, we derive policies that are optimally fair and simultaneously enjoy a small “price of fairness.” We illustrate the relative merits of our algorithmic framework with a case study on contextual bandits for warfarin dosing where we are concerned with the cost of exploration across multiple races and age groups. This paper was accepted by David Simchi-Levi, data science. Funding: This work was supported by the National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 1727239]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01985 .