Pure Equilibrium Research Articles

Simple collective equilibria in stopping games

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.

Perseverance and suspense in tug-of-war

We study a tug-of-war game between two players using the lottery contest success function (CSF) and a quadratic cost (of effort) function. We construct a pure strategy symmetric Markov perfect equilibrium of this game, show that it is unique, and provide closed-form solutions for equilibrium strategies and values. In stark contrast to a model of tug-of-war with an all-pay auction CSF, players exert positive efforts until the very last battle in this equilibrium. We deliver a set of empirically appealing results on effort dynamics.

The Welfare Impacts of Large Urban Noise Reductions: Implications from Household Sorting in Vienna

We develop a pure characteristics equilibrium sorting model to recover estimates of willingness to pay (WTP) for both marginal and non-marginal changes in urban noise exposure. Using data from Vienna, Austria, we provide several new insights in the urban noise literature. First, we demonstrate the importance of considering general equilibrium feedback effects following large changes in noise levels. We document impacts to residents in policy targeted and non-targeted locations due to changes in both noise and equilibrium prices. Second, we confirm evidence of the importance of noise thresholds with significant and increasing negative impacts associated with increases in area covered by high levels of noise at 50 dB and 60 dB thresholds, respectively. Finally, we use an equilibrium sorting model to predict new price patterns and welfare implications following hypothetical policy changes that alter the distribution and intensity of nighttime noise in Vienna and are relevant to other urban settings seeking to reduce noise levels. Our work additionally provides a roadmap for conducting similar equilibrium sorting work in data limited settings outside the U.S.

Sampling Dynamics and Stable Mixing in Hawk-Dove Games

The hawk-dove game admits two types of equilibria: asymmetric pure equilibria in which players in one population play ‘hawk’ and players in the other population play ‘dove’, and a symmetric mixed equilibrium. The existing literature on dynamic evolutionary models show that populations will converge into playing one of the asymmetric pure equilibria from any initial state. By contrast, we show that under plausible sampling dynamics, in which agents occasionally revise their actions by observing either opponents’ behavior or payoffs in a few past interactions, can induce the opposite result: global convergence to the symmetric mixed equilibrium.

Linear spaces of games on the unit square with pure equilibrium points

The set of all linear spaces of continuous two-person zero-sum games on the unit square with pure equilibrium points is considered. It is shown that the set contains maximal linearspaces of any finite dimension greater than three.

Option values in sequential auctions with time-varying valuations

We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are not necessarily efficient, but we show that when bidder valuations satisfy a certain constraint, an efficient equilibrium always exists. This result may be extended to a model with arrivals of bidders. We show how the equilibrium allocation, bids, and bidder utilities are calculated in the general case. We prove constructively that a pure subgame-perfect equilibrium always exists, and show how all pure equilibria can be found by the method of option values

A complete folk theorem for finitely repeated games

This paper analyzes the set of pure strategy subgame perfect Nash equilibria of any finitely repeated game with complete information and perfect monitoring. The main result is a complete characterization of the limit set, as the time horizon increases, of the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely repeated game. This model includes the special case of observable mixed strategies.

Nonatomic Game with General Preferencees on Returns

We study nonatomic games in which players' choices are guided by general preferences. Rather than ones over actions while also under influences of player-action profiles, we let the preferences be over returns received by individual players and let the returns be then linked to all players' actions. Our modeling choice has rendered otherwise standard analysis quite fruitful. Not only can we establish equilibrium existence results, but we can also simultaneously derive the upper hemi-continuity of equilibrium sets with respect to the return function and players' preference profile. Advances concerning pure equilibria can also be made on a setting involving a rich set of players, cruder traits, and an externality between semi-anonymity and anonymity.

Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon

Models of adaptive bet-hedging commonly adopt insights from Kelly’s famous work on optimal gambling strategies and the financial value of information. In particular, such models seek evolutionary solutions that maximize long-term average growth rate of lineages, even in the face of highly stochastic growth trajectories. Here, we argue for extensive departures from the standard approach to better account for evolutionary contingencies. Crucially, we incorporate considerations of volatility minimization, motivated by interim extinction risk in finite populations, within a finite time horizon approach to growth maximization. We find that a game-theoretic competitive optimality approach best captures these additional constraints and derive the equilibria solutions under straightforward fitness payoff functions and extinction risks. We show that for both maximal growth and minimal time relative payoffs, the log-optimal strategy is a unique pure strategy symmetric equilibrium, invariant with evolutionary time horizon and robust to low extinction risks.

Supply chain encroachment with quality decision and different power structures

This paper studies a supply chain with manufacturer encroachment and different power structures where product quality is an endogenous decision. We investigate the effects of encroachment and power structure on quality and profits for chain members. Employing a game-theoretic approach, we find that, first, in a manufacturer-led supply chain, encroachment makes both manufacturer and retailer better off when the quality investment efficiency is relatively high. And, the manufacturer’s profit exhibits nonmonotonicity with respect to the extent of consumers acceptance on the direct channel in a retailer-led setting. Second, our result shows that the pure equilibrium outcomes are driven by the quality investment efficiency and the extent of consumers’ acceptance on the direct channel. An interesting result is that, for the manufacturer, establishing encroachment channel and occupying the leader position simultaneously are always not the optimal choice. Additionally, the options of encroaching and striving for leader position can lead to lose-win, win-win, and win-lose situations for the manufacturer and the retailer. Finally, a prisoner’s dilemma may occur with a low quality investment efficiency, a moderately fixed encroachment cost and a high extent of consumers’ acceptance on the direct channel when a fixed encroachment cost is considered.

Invariant expressions for linear complex mechanisms: Single-step substance case

We generalize the results on invariances found for linear two-step mechanisms within our joint kinetics approach. A general invariant expression for any linear complex mechanism with at least two single-step substances is obtained, from corrected ratios of the concentration profiles of single-step substances.The invariant expression consist of the product of three factors of different nature:•A non-thermodynamic factor: the ratio of kinetic coefficients of different chemical reactions.•A thermodynamic factor: the pure or apparent equilibrium constant of a sub-mechanism within the complex mechanism.•An “experimental” factor, defined by the initial conditions of the two experiments needed to determine the invariant expression.The relationship between the structure of the linear complex mechanism and the peculiarities of the invariant expression obtained are presented.A mathematical demonstration of the invariant expression is given. The demonstration is based on an invariant expression from reciprocal experiments, related to Onsager’s reciprocal relations.

On the Cooling-to-Space Approximation

AbstractThe cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.

Taking Turns in Continuous Time

This paper studies the impact of continuous time interactions on the dynamics of battle of the sexes games with laboratory experiments. In discrete time battle of the sexes games, players often interact with alternating strategies and switch between two pure Nash equilibria, which is difficult to coordinate in continuous time because the players must determine both the order of alternations and how long to remain at each pure equilibrium. Overall, laboratory subjects behave differently in the two time environments. Although the continuous time interactions accelerate the initial convergence to one of the pure strategy equilibria and divergence from mismatches, they undermine the subjects' subsequent ability to coordinate moves from one equilibrium to the other. Compared to the alternating pattern in discrete time, the pattern in continuous time is unstable and diverse, and the transitions are mainly motivated by the disadvantaged subjects. The difficulty in alternation also slows the learning process in continuous time.

Dynamic Pricing for Power Control in Remote State Estimation

This paper considers the remote state estimation with multiple sensors. Each sensor transmits its sensing data to a remote estimator over a shared channel, where simultaneous transmissions are allowed. Regrading the transmission of other sensors as interference signals, the system designer should coordinate the sensors appropriately in order to maximize the overall estimation performance. Motivated by microeconomics, we treat sensors as self-interested power buyers under different unit prices announced by the system designer. Accordingly, the strategic interactions among sensors are formulated in a non-cooperative game, upon which the existence and uniqueness of a pure equilibrium solution are proved. Even if the game admits a conflict of interests among sensors, under well-designed prices, the game outcome aligns with the global optimal solution. We also devise an algorithm to compute these prices with simple iterations, which is given in explicit forms for ease of implementation. Numerical examples are given to demonstrate the developed results.

3.8 μm Imaging of 400–600 K Brown Dwarfs and Orbital Constraints for WISEP J045853.90+643452.6AB

Abstract Half of the energy emitted by late-T- and Y-type brown dwarfs emerges at 3.5 ≤ λ μm ≤ 5.5. We present new L′ (3.43 ≤ λ μm ≤ 4.11) photometry obtained at the Gemini North telescope for nine late-T and Y dwarfs, and synthesize L′ from spectra for an additional two dwarfs. The targets include two binary systems that were imaged at a resolution of 0.″25. One of these, WISEP J045853.90+643452.6AB, shows significant motion, and we present an astrometric analysis of the binary using Hubble Space Telescope, Keck Adaptive Optics, and Gemini images. We compare λ ∼ 4 μm observations to models, and find that the model fluxes are too low for brown dwarfs cooler than ∼700 K. The discrepancy increases with decreasing temperature, and is a factor of ∼2 at T eff = 500 K and ∼4 at T eff = 400 K. Warming the upper layers of a model atmosphere generates a spectrum closer to what is observed. The thermal structure of cool brown dwarf atmospheres above the radiative-convective boundary may not be adequately modeled using pure radiative equilibrium; instead heat may be introduced by thermochemical instabilities (previously suggested for the L- to T-type transition) or by breaking gravity waves (previously suggested for the solar system giant planets). One-dimensional models may not capture these atmospheres, which likely have both horizontal and vertical pressure/temperature variations.

Adsorption isotherms of CO2 – CH4 binary mixture using IAST for optimized ECBM recovery from sub-bituminous coals of Jharia coalfield: an experimental and modeling approach

ABSTRACTPrediction of adsorption equilibria of methane (CH4)/carbon dioxide (CO2) on coal at various feed gas composition is essential for the commercial development of primary and enhanced coalbed methane (ECBM) recovery by CO2 sequestration from coal reservoirs. In this article, an attempt is made to determine the adsorption equilibria of CH4 and CO2 mixture over a wide range of pressure and free gas compositions with the help of developed computational approach using the Ideal Adsorption Solution theory (IAST) for multicomponent adsorption. The advantage of the model is that it can predict the adsorption equilibrium of the mixture from the pure gas equilibrium data. Considering the complex adsorption during gas transportation and efficient gas injection modes at constant pressure or constant composition, the two different computational approaches were developed to solve the iterative calculation of IAST, i.e. constant mole fraction with variable pressure (P = 0 to 1000 psi) and constant pressure with mole fraction as a variable (y = 0 to 1). Individual adsorption isotherm of CH4 and CO2 for the two different sub-bituminous coal samples was determined up to a pressures of 1250 psi. Pure gas isotherms reveal that volume wise CO2 has 2.00 to 2.63 times more adsorption capacity than CH4 for the samples respectively. Computational model developed using ideal solution theory can predict the adsorbed gas volume at any pressure on the experimentally studied samples collected from Indian CBM fields. The developed computational code using MATLAB© software was validated using the binary adsorption data for the two coal samples from global CBM fields published in the literatures, with calculated error lying within the permissible limit.

Non-Cooperative Game of Throughput and Hash Length for Adaptive Merkle Tree in Mobile Wireless Networks

The restricted resources of mobile wireless networks such as limited bandwidth have resulted in stringent requirements on the available quality of service (QoS). To enhance the communication performance, mobile nodes attempt to optimize the available bandwidth of wireless networks, which, however, makes them vulnerable to the malicious attacks of adversaries owing to the open and mobile context. Furthermore, improving the security level of the communication consumes bandwidth and thus degrades the communication quality. In order to harmonize the QoS and security, in this paper, the two conflicting terms “communication player” and “security player” are considered as two individual players and are balanced using game theory. Furthermore, we construct a non-cooperative game model, wherein the utilities of the communication player and security player are maximized by controlling the number of nodes transmitted and the length of hash, respectively. We formulate the utility functions of the communication player with respect to the throughput as well as the security level of the Merkle tree for the security player. This paper considers complete information game and incomplete information game, for which we theoretically determine the pure strategy Nash equilibrium and the pure strategy Bayesian Nash equilibrium, respectively. Extensive numerical calculations are performed to comprehensively investigate the utilities of each player and the Nash equilibrium for various combinations of the concerned parameters. The results show that the presented theoretical game approach enables a mobile node to adaptively perform specific actions based on the derived Nash equilibrium. With the obtained Nash equilibrium values, both communication player's and security player's utilities reach to the maximum so that satisfactory communication quality can be realized without compromising the security.

A duopoly preemption game with two alternative stochastic investment choices

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover.

Carbon Monoliths by Assembling Carbon Spheres for Gas Adsorption

We report high-surface area, hierarchical pore structured, and robust activated carbon discs (ACDs) prepared via the assembly of micron-sized carbon spheres with mesophase pitch in a low-pressure foaming and carbonization process. The carbon disc ACDCS75 with the largest specific surface area (1338 m(2).g(-1)) was obtained from a blend of 75 wt % carbon spheres and 25 wt % mesophase pitch, and this ACD had a bulk density of 0.62 g.cm(3) and a high compressive strength of 26.3 MPa. A nitrogen-doped ACDCS75 disc was prepared by postcarbonization ammonia treatment to study the effect of nitrogen-containing surface functional groups on the uptake of CO2 on ACDs. The adsorption of pure fluids CO2, CH4, and N-2 were measured at temperatures of 298, 308, and 318 K at pressures from 6 to 3496 kPa for CO2, pressures from 9 to 3996 kPa for CH4, and pressures from 7 to 3994 kPa for N-2 using a high-pressure gravimetric apparatus (Belsorp-BG). The equilibrium adsorption capacities of ACDCS75 measured at 298 K and pressure close to 1000 kPa were 5.67 mmol.g(-1) CO2, 3.60 mmol.g(-1) CH4, and 2.09 mmol.g(-1) N-2, and at 3500 kPa were 6.16 mmol.g(-1) CO2, 4.42 mmol.g(-1) CH4, and 3.18 mmol.g(-1) N-2. After ammonia treatment the capacities of N-ACDCS75 at 298 K and 1000 kPa were 6.22 mmol.g(-1) CO2, 3.70 mmol.g(-1) CH4, and 1.98 mmol.g(-1) N-2, and at 3500 kPa were 7.16 mmol.g(-1) CO2, 4.87 mmol.g(-1) CH4, and 3.32 mmol.g(-1) N-2. The pure gas equilibrium adsorption capacities were regressed to Toth and Langmuir models, and the uptake of components from gas mixtures was predicted using an ideal selectivity to make a preliminary evaluation of the potential to use these ACDs for gas separation. After N-doping the predicted changes in selectivities at 298 K and 100 kPa were from 6.0 to 7.2 for CO2 over N-2 and 2.8 to 3.3 for CH4 over N-2 on ACDCS75 compared to on N-ACDCS75.

Channel coordination using options contract under simultaneous price and inventory competition

In this paper we demonstrate that options contract coordinates single supplier - multiple buyer supply chain network and can eliminate channel conflict stemming from simultaneous price and inventory competition. We show that a pure strategy unique Nash equilibrium exists for buyers’ game and the supplier is able to coordinate the entire supply chain. Our analysis further indicates that options contract provides the supplier with better flexibility in terms of profit allocation compared to buyback contract. We identify a key limitation of this contract: it can coordinate a supply chain only with a limited number of buyers.