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Shiv Nadar University

I examine the effect of decision-making processes on the dynamics of bargaining over a fixed pie by comparing the share received when individuals are subject to reference-dependent preferences, loss-aversion, and probability-weighting, to the share they would receive on choosing by maximising expected utility instead. I show that: (i) reference-dependent preferences are unambiguously advantageous, (ii) loss-aversion does not have any effect, and (iii) probability-weighting is unambiguously disadvantageous. Finally, when these three features come together so that the decision-making process is described by cumulative prospect theory, then a higher share is obtained if and only if the advantage conferred by reference-dependent preferences is stronger than the disadvantage imposed by probability-weighting, and I present a precise necessary and sufficient condition that expresses this trade-off. © 2022 Elsevier B.V.

Economics

(SoHSS) School of Humanities and Social Sciences

Journal of Economic Dynamics and Control

Expected utility versus cumulative prospect theory in an evolutionary model of bargaining

I study the evolutionary stability of behavioural rules in a bargaining game. Each individual bargains in a pairwise manner with all other individuals over the division of a pie of fixed size by claiming a share for himself; individuals in a pair receive their respective claims if and only if the sum of the claims does not exceed unity. Each individual is associated with a behavioural rule which determines the share he chooses to claim. A behavioural rule is a correspondence that maps from a set of demands that were claimed by individuals in the recent history of the game into a set of shares, and each share in the latter set is chosen by the individual with positive probability. The evolutionary fitness of a behavioural rule is determined by the shares obtained by individuals who follow that particular rule, and fitter behavioural rules are selected over rules that are less fit. A state, i.e. a profile of claims made by the individuals in the population, is defined to be stable (neutrally stable) if the population continues to be comprised only of the incumbent behavioural rules (all incumbent behavioural rules continue to exist) even in the face of an appearance of a mutant behavioural rule. I formalise this in terms of two conditions. Firstly, internal stability requires the incumbent behavioural rules in the population to be equally fit. Secondly, external stability (neutral external stability) requires incumbent behavioural rules to be fitter (to not be less fit) than any mutant behavioural rule. I show that: (i) a necessary condition for stability of a state is that the state must be such that each individual responds by claiming a time-invariant share of the pie, and (ii) the state where all individuals demand half of the pie is the only state that is both internally stable and neutrally externally stable. © 2021 Elsevier B.V.

Fulltext

Journal of Economic Behavior and Organization

Evolutionary stability of behavioural rules in bargaining

We study the stable market outcome that evolves when firms, that operate in a spatially differentiated duopolistic market, recurrently choose prices and quantities via an imitation dynamic. In particular, given that firms choose both prices and quantities, we do not explicitly impose market clearing. We find that: (i) a market-clearing outcome always belongs to the set of stable long-run outcomes, (ii) when the level of market differentiation is low, non-market-clearing outcomes (with excess supply as well as excess demand) are also stable, (iii) when the level of market differentiation is not too high or too low, the stable long-run outcomes imply market clearing at prices above monopoly level, and (iv) when the level of market differentiation is high, the stable long-run outcome implies market clearing at the monopoly price. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

World University root node

Dynamic Games and Applications

Evolution of Behavior When Duopolists Choose Prices and Quantities

We study the stable market outcome that evolves in a spatially differentiated market when price-competing firms choose actions by imitation of the most profitable firm. We compare and contrast the stable outcomes under two imitation procedures: one, where each firm immediately imitates the most profitable firm, and the other when a firm imitates another firm only if it is more profitable while being “sufficiently similar” (in context of the market segment it operates in) or “sufficiently close”. In either case, the symmetric pure strategy Nash equilibrium is always a stable outcome. However, when imitation of the most profitable firm is immediate and market differentiation is ‘moderate’, states with prices lower than the Nash equilibrium are also stable. In contrast, when imitation of the most profitable firm is more gradual and market differentiation is below a threshold, states with prices above the Nash equilibrium are also stable. Thus, while competitive evolutionary pressure in this imitation based model does result in the Nash equilibrium always being stable, other outcomes may be stable as well. Interestingly, the states that are stable under gradual imitation give the firms a higher profit than the stable states under immediate imitation. © 2017 Elsevier B.V.

Imitation and price competition in a differentiated market

Using data generated by extensive simulations of a process where individuals interact globally in a coordination game and iteratively imitate the action of the most successful individual in their local neighbourhood, we study the characteristics of the observation network and distribution of initial choices that facilitate (a speedy) convergence to efficient coordination. Knowing these characteristics is crucial when intervening in social network structures with the intention to nudge society to a socially preferred outcome. The most important factor appears to be the share of individuals that are initially seeded with the socially desirable action. Only for a small window of this share, other factors, including the degree distribution in the network and the segregation of individuals using similar actions, have an influence on the dynamic process of achieving efficient coordination. Moreover, networks possessing the properties of a scale-free network are more likely to yield an efficient outcome compared to small-world networks. © 2015, The Author(s).

Network Characteristics Enabling Efficient Coordination: A Simulation Study

We study the evolution of imitation behaviour in a differentiated market where firms are located equidistantly on a (Salop) circle. Firms choose price and quantity simultaneously, leaving open the possibility for non-market-clearing outcomes. The strategy of the most successful firm is imitated. Behaviour in the stochastically stable outcome depends on the level of market differentiation and corresponds exactly with the Nash equilibrium outcome of the underlying stage game. For high level of differentiation, firms end up at the monopoly outcome. For intermediate level of differentiation, they gravitate to a "mutually non-aggressive" outcome where price is higher than the monopoly price. For low level of differentiation, firms price at a mark-up above the marginal cost. Market-clearing always results endogenously. © 2015 Elsevier B.V.

Imitation by price and quantity setting firms in a differentiated market

Individuals are randomly matched to play a 2X2 coordination game where the Pareto efficient and risk dominant equilibria differ. Players choose strategies by imitating the strategy of the most successful individual they observe. So, while individuals interact globally, their observation and hence imitation, as determined by their social network, may be local. When all individuals observe each other, the most successful individual in the entire population is imitated; here, in the stochastically stable state, the population coordinates on the Pareto-efficient outcome. While this outcome is always stochastically stable, even when observability is incomplete, the state where everyone plays the action of the risk-dominant equilibrium may be stochastically stable as well. Reasonably tight sufficient conditions for unique stochastic stability of the state where all coordinate on the Pareto-efficient equilibrium strategy include each individual observing at least four other individuals or when each individual observes the same number of other individuals. These properties are readily generalisable to larger mXm coordination games where the coordination outcomes can be Pareto-ranked. © 2014, Springer-Verlag Berlin Heidelberg.

International Journal of Game Theory

Coordination under global random interaction and local imitation

Inspired by the behavior in repeated guessing game experiments, we study adaptive play by populations containing individuals that reason with different levels of cognition. Individuals play a higher order best response to samples from the empirical data on the history of play, where the order of best response is determined by their exogenously given level of cognition. As in Young’s model of adaptive play, (unperturbed) play still converges to a minimal curb set. Random perturbations of the best response dynamic identifies the stochastically stable states. In Young’s model of adaptive play with simple best-responses, the set of stochastically stable states are sensitive to the sample size that individuals from a population can draw. In generic games with higher order best-responders in both populations, the sample size is rendered irrelevant in determination of the stochastically stable set. Perhaps counter-intuitively, higher cognition may actually be bad for both the individual with higher cognition and his parent population. © 2014, Springer-Verlag Berlin Heidelberg.