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on Game Theory |
| By: | Christos Papadimitriou; Kiran Vodrahalli; Mihalis Yannakakis |
| Abstract: | On-line firms deploy suites of software platforms, where each platform is designed to interact with users during a certain activity, such as browsing, chatting, socializing, emailing, driving, etc. The economic and incentive structure of this exchange, as well as its algorithmic nature, have not been explored to our knowledge; we initiate their study in this paper. We model this interaction as a Stackelberg game between a Designer and one or more Agents. We model an Agent as a Markov chain whose states are activities; we assume that the Agent's utility is a linear function of the steady-state distribution of this chain. The Designer may design a platform for each of these activities/states; if a platform is adopted by the Agent, the transition probabilities of the Markov chain are affected, and so is the objective of the Agent. The Designer's utility is a linear function of the steady state probabilities of the accessible states (that is, the ones for which the platform has been adopted), minus the development cost of the platforms. The underlying optimization problem of the Agent -- that is, how to choose the states for which to adopt the platform -- is an MDP. If this MDP has a simple yet plausible structure (the transition probabilities from one state to another only depend on the target state and the recurrent probability of the current state) the Agent's problem can be solved by a greedy algorithm. The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), while NP-hard, has an FPTAS. These results generalize, under mild additional assumptions, from a single Agent to a distribution of Agents with finite support. The Designer's optimization problem has abysmal "price of robustness", suggesting that learning the parameters of the problem is crucial for the Designer. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.06117&r=all |
| By: | Meinhardt, Holger Ingmar |
| Abstract: | Based on results discussed by Meinhardt (2013), which presents a dual characterization of the prekernel by a finite union of solution sets of a family of quadratic and convex objective functions, we could derive some results related to the single-valuedness of the pre-kernel. Rather than extending the knowledge of game classes for which the pre-kernel consists of a single point, we apply a different approach. We select a game from an arbitrary game class with a single pre-kernel element satisfying the non-empty interior condition of a payoff equivalence class, and then establish that the set of related and linear independent games which are derived from this pre-kernel point of the default game replicates this point also as its sole pre-kernel element. Hence, a bargaining outcome related to this pre-kernel element is stable. Furthermore, we establish that on the restricted subset on the game space that is constituted by the convex hull of the default and the set of related games, the pre-kernel correspondence is single-valued, and therefore continuous. In addition, we provide sufficient conditions that preserve the pre-nucleolus property for related games even when the default game has not a single pre-kernel point. Finally, we apply the same techniques to related solutions of the pre-kernel, namely the modiclus and anti-pre-kernel, to work out replication results for them. |
| Keywords: | Transferable Utility Game, Pre-Kernel, Pre-Nucleolus, Anti-Pre-Nucleolus, Modiclus, Uniqueness of the Pre-Kernel, Convex Analysis, Fenchel-Moreau Conjugation, Indirect Function, Stability Analysis. |
| JEL: | C71 |
| Date: | 2020–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:102676&r=all |
| By: | Matthijs van Veelen (University of Amsterdam) |
| Abstract: | Most of the literature on the evolution of human pro-sociality looks at reasons why evolution made us not play the Nash equilibrium in prisoners’ dilemmas or public goods games. We suggest that in order to understand human morality, and human prosocial behaviour, we should look at reasons why evolution made us not play the subgame perfect Nash equilibrium in sequential games, such as the ultimatum game and the trust game. The “rationally irrational†behavior that can evolve in those games is a better match with actual human behaviour, including ingredients of morality such as honesty, responsibility, and sincerity, and also less nice properties, such as anger, as well as the incidence of conflict. Moreover, it can not only explain why humans have evolved to know wrong from right, but also why other animals, with similar population structures and similar rates of repetition, have not evolved the morality that humans have. |
| JEL: | C73 |
| Date: | 2020–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20200063&r=all |
| By: | Rogna, Marco; Vogt, Carla |
| Abstract: | Obtaining significant levels of cooperation in public good and environmental games, under the assumption of players being purely selfish, is usually prevented by the problem of freeriding. Coalitions, in fact, generally fail to be internally stable and this cause a serious underprovision of the public good together with a significant welfare loss. The assumption of relational preferences, capable of better explaining economic behaviors in laboratory experiments, helps to foster cooperation, but, without opportune transfers scheme, no substantial improvements are reached. The present paper proposes an optimal transfers scheme under the assumption of players having Fehr and Schmidt (1999) utility functions, whose objective is to guarantee internal stability and to maximize the sum of utilities of coalition members. The transfers scheme is tested on a public good contribution game parameterized on the data provided by the RICE model and benchmarked with other popular transfers scheme in environmental economics. The proposed scheme outperforms its benchmarking counterparts in stabilizing coalitions and sensibly increases cooperation compared to the absence of transfers. Furthermore, for high but not extreme values of the parameter governing the intensity of dis-utility from disadvantageous inequality, it manages to support very large coalitions including three quarters of all players. |
| Keywords: | climate policy,coalitions,inequality aversion,RICE model,transfers scheme |
| JEL: | C72 D63 H41 Q54 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:865&r=all |
| By: | Castagnetti, Alessandro (University of Warwick); Proto, Eugenio (University of Glasgow) |
| Abstract: | Anger is an important driver in shaping economic activities, particularly in instances that involve strategic interactions between individuals. Here we test whether anger impairs the capacity to think strategically, and we analyze the implications of our result on bargaining and cooperation games. Accordingly, with a preregistered experiment (Experiment 1), we externally induce anger to a subgroup of subjects following a standard procedure that we verify by using a novel method of text analysis. We show that anger can impair the capacity to think strategically in a beauty contest game. Angry subjects choose numbers further away from the Nash equilibrium, and earn significantly lower profits. A structural analysis estimates that there is an increase in the share of level-zero players in the treated group compared to the control group. Furthermore, with a second preregistered experiment (Experiment 2), we show that this effect is not common to all negative emotions. Sad subjects do not play significantly further away from the Nash equilibrium than the control group in the same beauty contest game of Experiment 1, and sadness does not lead to more level-zero play. |
| Keywords: | anger, induced emotions, strategic interactions, beauty-contest |
| JEL: | C92 D90 D91 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp13661&r=all |
| By: | Ohnishi, Kazuhiro |
| Abstract: | This paper first examines a price-setting mixed duopoly game with production subsidies where a public firm acts as a leader against a private firm. Second, the paper examines a price-setting duopoly game with production subsidies where the public firm remains a leader after privatization. Third, the paper compares the equilibrium values for private leadership with those for public leadership. |
| Keywords: | Price competition; Subsidy; Privatization; Mixed Stackelberg duopoly; Privatized Stackelberg duopoly |
| JEL: | C72 D21 L32 |
| Date: | 2020–09–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:102847&r=all |
| By: | Diego Zabaljauregui |
| Abstract: | The topics treated in this thesis are inherently two-fold. The first part considers the problem of a market maker optimally setting bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. This stochastic control problem under partial information is solved by means of stochastic filtering, control and PDMPs theory. The value function is characterized as the unique continuous viscosity solution of its dynamic programming equation and numerically compared with its full information counterpart. The optimal full information spreads are shown to be biased when the exact market regime is unknown, as the market maker needs to adjust for additional regime uncertainty in terms of PnL sensitivity and observable order flow volatility. The second part deals with numerically solving nonzero-sum stochastic impulse control games. These offer a realistic and far-reaching modelling framework, but the difficulty in solving such problems has hindered their proliferation. A policy-iteration-type solver is proposed to solve an underlying system of quasi-variational inequalities, and it is validated numerically with reassuring results. Eventually, the focus is put on games with a symmetric structure and an improved algorithm is put forward. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. The algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of the currently available theory. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.06521&r=all |
| By: | Treb Allen; Costas Arkolakis; Xiangliang Li |
| Abstract: | In this note, we consider a broad class of network models where a large number of heterogeneous agents simultaneously interact in many ways. We provide an iterative algorithm for calculating an equilibrium and offer sufficient and “globally necessary” conditions under which the equilibrium is unique. The results arise from a multi-dimensional extension of the contraction mapping theorem which allows for the separate treatment of the different types of interactions. We illustrate that a wide variety of heterogeneous agent economies – characterized by spatial, production, or social networks – yield equilibrium representations amenable to our theorem's characterization. |
| JEL: | C6 D85 E23 F4 O18 R13 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:27837&r=all |
| By: | Komal Malik; Debasis Mishra |
| Abstract: | We consider a combinatorial auction model where preferences of agents over bundles of objects and payments need not be quasilinear. However, we restrict the preferences of agents to be dichotomous. An agent with dichotomous preference partitions the set of bundles of objects as acceptable} and unacceptable, and at the same payment level, she is indifferent between bundles in each class but strictly prefers acceptable to unacceptable bundles. We show that there is no Pareto efficient, dominant strategy incentive compatible (DSIC), individually rational (IR) mechanism satisfying no subsidy if the domain of preferences includes all dichotomous preferences. However, a generalization of the VCG mechanism is Pareto efficient, DSIC, IR and satisfies no subsidy if the domain of preferences contains only positive income effect dichotomous preferences. We show the tightness of this result: adding any non-dichotomous preference (satisfying some natural properties) to the domain of quasilinear dichotomous preferences brings back the impossibility result. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.12114&r=all |
| By: | Michael J. Campbell; Vernon L. Smith (Chapman University) |
| Abstract: | We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward /punishment in the form of higher/lower payo transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude /resentment changes much more slowly than economic equilibrium (“quenched model†). Another model, in which economic equilibrium occurs over a much slower time than gratitude /resentment evolution (“annealed†model) is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A twoagent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1 􀀀 p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p i , i = 1; 2, exists for each agent. When p p i , agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payo is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties. |
| Keywords: | Agent Based Model, Bounded Rationality, Correlation Inequality, Humanomics, Phase Transition, Potential Game, Spin Glass |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-35&r=all |