Presence Of Multiple Equilibria Research Articles

Multiple regimes in the preferences for redistribution

AbstractThis paper provides novel evidence of nonlinearities in the formation of preferences for redistribution by uncovering evidence of multiple regimes consistent with the presence of multiple equilibria and multiple steady states. Using threshold regressions that account for the endogeneity of the threshold variable, countries are classified into three groups that share common characteristics. Finally, our analysis reveals substantial evidence of parameter heterogeneity in the coefficient estimates of threshold regressions.

The explosive value of the networks

Networks have always played a special role for human beings in shaping social relations, forming public opinion, and driving economic equilibria. Nowadays, online networked platforms dominate digital markets and capitalization leader-boards, while social networks drive public discussion. Despite the importance of networks in many economic and social domains (economics, sociology, anthropology, psychology, etc.), the knowledge about the laws that dominate their dynamics is still scarce and fragmented. Here, we analyse a wide set of online networks (those financed by advertising) by investigating their value dynamics from several perspectives: the type of law they follow, their geographic scope, and the relationship between economic value and financial value. The results show that the networks are dominated by strongly nonlinear dynamics. The existence of non-linearity is often underestimated in social sciences because it involves contexts that are difficult to deal with, such as the presence of multiple equilibria—some of which are unstable. Yet, these dynamics must be fully understood and addressed if we aim to understand the recent evolution in the economic, political and social milieus, which are precisely characterised by corner equilibria (e.g., polarisation, winner-take-all solutions, increasing inequality) and nonlinear patterns.

Two-Sided Competition Between On-Demand Service Platforms

On-demand service platforms compete for both workers and customers, forming a two-sided competition. In this paper, we study the game between two platforms implied by such a two-sided competition and examine how the characteristics of the embedded workers-customers subgame affect outcomes in equilibrium. Specifically, we consider two subgame settings: (i) workers and customers move sequentially and (ii) workers and customers move simultaneously. We find that these two settings yield different subgame outcomes. In the first setting, given any platform strategy profile, there is no subgame equilibrium such that both platforms have a positive market share. In the simultaneous-move setting, such subgame equilibria can exist, though not unique. In the presence of multiple equilibria, we show that under some refinement rules both settings (the sequential and simultaneous subgames) yield the same unique pure-strategy equilibrium. We discuss how these results shed light on the competitive dynamics of on-demand service platforms in practice.

A dynamic analysis of nash equilibria in search models with fiat money

We analyze the rise in the acceptability fiat money in a Kiyotaki–Wright economy by developing a method that can determine dynamic Nash equilibria for a class of search models with genuine heterogeneous agents. We also address open issues regarding the stability properties of pure strategy equilibria and the presence of multiple equilibria, numerical experiments illustrate the liquidity conditions that favor the transition from partial to full acceptance of fiat money, and the effects of inflationary shocks on production, liquidity, and trade.

Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games

This paper revisits the problem of how to select an equilibrium in a differential game in the case of multiplicity of Nash equilibria. Most of the previous applied dynamic games literature has considered pre-play negotiations between players, implicitly or explicitly, with the aim of reaching an agreement on the selection of the pair of strategies. The main objective of this paper is to determine what would be the equilibrium to be played without pre-play communications. We study the linear and nonlinear Markov perfect Nash equilibria for a class of well-known models in the literature if pre-play communications are eliminated. We analyze both symmetric and nonsymmetric strategies. We show that the nonlinear strategies are not always the optimal strategies implemented when pre-play communications are removed. We conclude that in the presence of multiple equilibria and without pre-play communications the equilibria actually implemented are symmetric piecewise linear Markov perfect Nash equilibria at least for a range of initial values of the state variable.

Collusion and heterogeneity of firms

We examine the impact of heterogeneous discounting on collusion in dynamic Bertrand competition. We show exactly when collusion can be sustained and how collusion would be organized efficiently with heterogeneous discounting. First, we show that collusion is possible if and only if the average discount factor exceeds a certain threshold, with or without capacity constraints. Next, we identify a dynamic pattern of market share that characterizes efficient collusion and obtain the unique long‐run prediction despite the presence of multiple equilibria. In the long run, the most patient firm and the most impatient firm tend to dominate the market.

Model Microvascular Networks Can Have Many Equilibria.

We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams. We demonstrate that the disparity between observed and predicted flow directions reported in previous studies might be attributable to the presence of multiple equilibria. We show that the pathway effect, in which hematocrit is steadily increased along a series of diverging junctions, has important implications for equilibrium discovery, and that our estimates of the number of equilibria supported by these networks are conservative. If a more complete description of the plasma skimming effect that captures red blood cell allocation at junctions with high feed hematocrit were to be obtained empirically, then the number of equilibria found by our approach would at worst remain the same and would in all likelihood increase significantly.

Social Responsibility, Human Morality and Public Policy

The evidence shows that in many important economic domains, many people are either predisposed to engage in `socially responsible actions' and/or required by regulations to do so. Examples include pollution abatement activity, behavior in a commons, and contributions to charity. We propose a general framework of analysis for modelling such actions and the role of public policy in encouraging these actions in an equilibrium setting. Multiple equilibria are endemic in these situations. We show that it is possible to conduct interesting and meaningful analysis in the presence of multiple equilibria. We examine the role of optimal public policy such as subsidies, taxes and direct government grants in engineering moves from less to more desirable equilibria. We highlight a new role for leadership contributions in facilitating moves between multiple equilibria. We also conduct a welfare analysis of the optimal mix between private and public actions.

Identification of Static and Dynamic Games of Incomplete Information with Multiple Equilibria in the Data

I study identification of games of incomplete information, both static and dynamic, when there are multiple equilibria in the data. In the case of static games, I show that if multiplicity disappears at a small subset of the support of the observables, payoffs are identified. All the equilibria of the model are also then identified. As \textit{payoff relevant} unobservables are an alternative explanation to multiple equilibria for observed correlation in player actions conditional on observables, I allow for this type of variable and show that as long as a conditional exclusion restriction on the distribution of the unobservables is satisfied, payoffs, equilibria and the distribution of the payoff relevant unobservable are identified. Additionally, letting $A$ be the number of choice alternatives, $N$ the number of players and $K$ the number of equilibria, as long as $A^N\geq K$, I show that equilibrium selection probabilities are also identified, a result that is useful for considering the effects of counterfactual experiments in the presence of multiple equilibria. I extend the framework to study identification in dynamic games. The static approach extends in a straightforward way to finite horizon (non-stationary) games, but not to the more common case of infinite horizon (stationary) games. I show that by making additional testable restrictions on the transition probabilities, a large class of stationary dynamic games are also identified.

The expectation effect of a fall in divorce costs

Under private information about spouse characteristics a fall in the cost of divorce has a direct divorce-increasing effect and an indirect effect through expectations about second-marriage spouse quality. The expectation effect reinforces the direct effect if the proportion of “good” spouse types is sufficiently large in couples with marginal match qualities – in the case of unimodal and symmetric match quality distributions, if “good” spouse types are in majority and the prospective benefit from finding a “good” spouse relative to the cost of divorce is initially large. Otherwise, expectations diminish and partially offset the rise in divorce. In the presence of multiple equilibria, the expectation effect can trigger a substantial short-run change in divorce.

Reference dependence, cooperation, and coordination in games

AbstractThe problems of how self-interested players can cooperate despite incentives to defect, and how players can coordinate despite the presence of multiple equilibria, are among the oldest and most fundamental in game theory. In this report, we demonstrate that a plausible and even natural specification of the reference outcome in a game simultaneously predicts systematic cooperation and defection in the Prisoner’s Dilemma, as well as equilibrium selection and out-of-equilibrium play in coordination games. The predictions hold even if players are purely self-interested, there are no salient labels, the game is played only once, and there is no communication of any kind. Furthermore, the predictions are unique, as opposed to the multiplicity of equilibria in the infinitely repeated Prisoner’s Dilemma and in coordination games. We apply experimental results to test the predictions of the model.

Book Reviews

Presents a model of a professional sports league that can display unsustainable runs—rapid improvements in a club's performance on the field, ice, or court that require implausibly large shifts in exogenous variables or parameters to fit traditional notions of profit-maximizing behavior—resulting from the presence of multiple equilibria. Discusses introducing unsustainable runs; casual evidence of unsustainable runs; a model of a professional sports league; a professional sports league model with unsustainable runs; unsustainable runs with revenue sharing the salary caps; and some empirical testing. Rockerbie is with the Department of Economics at the University of Lethbridge. Easton is with the Department of Economics at Simon Fraser University.

Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information

This paper studies the inference of interaction effects in discrete simultaneous games with incomplete information. We propose a test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals, or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also implement the test using data on radio programming of commercial breaks in the United States, and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives to coordinate and air commercials at the same time during rush hours and in smaller markets.

Association of aureolic acid antibiotic, chromomycin A3 with Cu2+ and its negative effect upon DNA binding property of the antibiotic

Here we have examined the association of an aureolic acid antibiotic, chromomycin A3 (CHR), with Cu(2+). CHR forms a high affinity 2:1 (CHR:Cu(2+)) complex with dissociation constant of 0.08 × 10(-10) M(2) at 25°C, pH 8.0. The affinity of CHR for Cu(2+) is higher than those for Mg(2+) and Zn(2+) reported earlier from our laboratory. CHR binds preferentially to Cu(2+) in presence of equimolar amount of Zn(2+). Complex formation between CHR and Cu(2+) is an entropy driven endothermic process. Difference between calorimetric and van't Hoff enthalpies indicate the presence of multiple equilibria, supported from biphasic nature of the kinetics of association. Circular dichroism spectroscopy show that [(CHR)(2):Cu(2+)] complex assumes a structure different from either of the Mg(2+) and Zn(2+) complex reported earlier. Both [(CHR)(2):Mg(2+)] and [(CHR)(2):Zn(2+)] complexes are known to bind DNA. In contrast, [(CHR)(2):Cu(2+)] complex does not interact with double helical DNA, verified by means of Isothermal Titration Calorimetry of its association with calf thymus DNA and the double stranded decamer (5'-CCGGCGCCGG-3'). In order to interact with double helical DNA, the (antibiotic)(2) : metal (Mg(2+) and Zn(2+)) complexes require a isohelical conformation. Nuclear Magnetic Resonance spectroscopy shows that the Cu(2+) complex adopts a distorted octahedral structure, which cannot assume the required conformation to bind to the DNA. This report demonstrates the negative effect of a bivalent metal upon the DNA binding property of CHR, which otherwise binds to DNA in presence of metals like Mg(2+) and Zn(2+). The results also indicate that CHR has a potential for chelation therapy in Cu(2+) accumulation diseases. However cytotoxicity of the antibiotic might restrict the use.

Spectroscopic studies on U(VI)-salicylate complex formation with multiple equilibria

Abstract This study investigates multiple equilibria related to the formation of the U(VI)-salicylate complex in a pH range of 3.0–5.5 using UV-Vis absorption and fluorescence measurement techniques. The absorbance changes at the characteristic charge-transfer bands of the complex were monitored, and the results indicated the presence of multiple equilibria and the formation of both 1:1 and 1:2 (U(VI):salicylate) complexes possessing bi-dentate chelate structures. The determined step-wise formation constants (log K 1:1 and log K 1:2) are as follows: 12.5 ± 0.1 and 11.4 ± 0.2 for salicylate, 11.2 ± 0.1 and 10.1 ± 0.2 for 5-sulfosalicylate, and 12.4 ± 0.1 and 11.4 ± 0.1 for 2,6-dihydroxybenzoate, respectively. The molar absorptivities of the complexes are also provided. Furthermore, time-resolved laser-induced luminescence spectra of U(VI) species demonstrate the presence of both a dynamic and static quenching process upon the addition of a salicylate ligand. Particularly for the luminescent hydroxouranyl species, a strong static quenching effect is observed. The results suggest that both the UO2(HSal)+ and the U(VI)–Sal chelate complexes serve as ground-state complexes that induce static quenching. The Stern–Volmer parameters were derived based on the measured luminescent intensity and lifetime data. The static quenching constants (log K S) obtained are 3.3 ± 0.1, 4.9 ± 0.1, and 4.4 ± 0.1 for UO2 2+, (UO2)2(OH)2 2+ and (UO2)3(OH)5 +, respectively.

Quality Traps in Localized Competition

A wide spectrum of technologies, producing a vast array of product qualities, coexists in modern markets today. Many of these markets are also characterised by what is commonly known as localized competition that refers to a special industrial structure in which different firms compete directly with different groups of rivals. We explore the endogenous choice of product quality in localized competition such that the choice of product quality by a seller has effects only on those rivals who share the common market segment. In the proposed model multiple equilibria may occur and the present analysis may be seen as a rationalization for the idea that a market segment may become trapped in a “low-quality” equilibrium. In the presence of multiple equilibria and the quality trap, the industrial policy may have a welfare-enhancing role in coordinating expectations. We then extend the model to highlight the conditions that can preclude the possibility of the quality trap in localised competition.

Emergência de convenções sociais: uma análise a partir da simulação de interações descentralizadas caracterizadas pela disposição à imitação de comportamento

Considerando que a existência de convenções sociais é relevante sobre o comportamento econômico dos indivíduos, faz-se necessário explicitar suas causas e seu processo de formação. Em particular estudamos situações onde a presença de equilíbrios múltiplos e a possibilidade de irreversibilidade de uma tomada de decisão importam. Para isto aprofundamos a tradição dos estudos sobre processos evolucionários descentralizados caracterizados por path-dependence. Utilizamos a hipótese de que indivíduos com racionalidade limitada imitam em algum grau um comportamento predominante observado para construirmos um programa de simulação. Observamos a emergência de estruturas de unanimidade ou de maiorias e aplicamos nossos resultados às teorias da emergência da moeda e da formação de padrões tecnológicos.

'Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information', Second Version

This paper studies the inference of interaction effects (impacts of players' actions on each other's payoffs) in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also show how to extend our arguments to identify signs of interaction effects when private signals are correlated. We provide Monte Carlo evidence of the test's good performance in finite samples. We then implement the test using data on radio programming of commercial breaks in the U.S., and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives

Sharp Identification Regions in Models With Convex Moment Predictions

We provide a tractable characterization of the sharp identi…cation region of the parameters � in a broad class of incomplete econometric models. Models in this class have set valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables. In short, we call these models with convex moment predictions. Examples include static, simultaneous move …nite games of complete and incomplete information in the presence of multiple equilibria; best linear predictors with interval outcome and covariate data; and random utility models of multinomial choice in the presence of interval regressors data. Given a candidate value for �; we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly de…ned random set.

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information

This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance in finite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.