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on Game Theory |
| By: | Pradeep Dubey; Siddhartha Sahi |
| Abstract: | Consider a noncooperative game at whose outcomes commodities accrue to players, which are both valued by them and susceptible to transfer between them. In this situation, outcome-contingent transfers of commodities form a natural schema for incentivizing cooperation, potentially leading to Nash Equilibria (NE) that are better for all players. However, as in the folk theorem for repeated games, an embarrassingly large set of NE may be sustainable via transfers. The main source for this pathology is the possibility of a "threat", which can be understood as an "off-shell" transfer, i.e. a transfer that is contracted to take place at an outcome that is not actually being reached with positive probability at the strategy selection under consideration. Our goal is to restore the discriminatory nature of NE by means of a simple idea. We call an NE of the post-transfers game transparent if there are no off-shell transfers. This can also be viewed via the lens of "credibility", of something being seen in order to be believed. Among the transparent equilibria it is natural to focus on those that Pareto-improve players’ payoffs as much as possible with respect to a status quo NE of the pre-transfer game. In addition, if a social welfare function is specified, then one may ask for points in the Pareto-set that maximize welfare and achieve the gains to transfer. By way of illustration we analyze three classical non-cooperative games. These are the Centipede Game, Contest, and the Prisoners’ Dilemma; the last of which we discuss in some detail. |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:nys:sunysb:20-10&r=all |
| By: | Francesco Caruso (Università di Napoli Federico II); Maria Carmela Ceparano (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEF) |
| Abstract: | In two-player non-cooperative games whose strategy sets are Hilbert spaces, in order to approach Nash equilibria we are interested in the affine relaxations of the best response algorithm (where a player's strategy is exactly a best response to the strategy of the other player that comes from the previous step, sometimes called as "fictitious play"). For this purpose we define a class of games, called ratio-bounded games, that relies on explicit assumptions on the data and that contains large classes of games already known in literature, both in finite and in infinite dimensional setting: extended quadratic games including potential and antipotential games, non-quadratic games with a bilinear interaction, and linear state differential games. We provide a classification of the ratio-bounded games in four subclasses such that, for each of them, the following issues are examined: the existence and uniqueness of Nash equilibria, the convergence of affine relaxations of the best response algorithm and the estimation of related errors. In particular, the results on convergence of convex relaxations of the best response algorithm include those obtained for zero-sum games in Morgan [Int. J. Comput. Math., 4 (1974), pp. 143-175], and the results on convergence of affine non-convex relaxations include those obtained for non-zero-sum games in Caruso, Ceparano, Morgan [SIAM J. Optim., 30 (2020), pp. 1638-1663]. |
| Keywords: | Two-player non-cooperative game; Nash equilibrium; existence and uniqueness; fixed point; contraction mapping; non-expansive mapping; super monotone operator; best response algorithm; convex relaxation; affine non-convex relaxation; convergence and error bound. |
| Date: | 2020–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:593&r=all |
| By: | Pazhanisamy, R.; Selvarajan, E. |
| Abstract: | Various attempts have been made to reveal the impact of corona virus on the global economy through interdisciplinary approaches. The ultimate logic behind the strategies adopted by leaders of various economies regarding the first level policy response of lockdown and the and the end level solution through low cost responsive vaccine with zero negative externalities has raised a self-sustainable crux which raise the question of why the world is not yet reached “Global Nash Equilibrium” in which all countries may reach a Covid fear free economy. In this context the present is attempt to fill this gap by developing a game theory based model. Keeping the present market structure for the vaccine and it is also predicted that demand curve for the vaccine even if it is in competitive price level become flat. |
| Keywords: | Non cooperative Games,Nash Equilibrium,Global Equilibrium,lockdown Economics,Demand Curve for Covid Vaccine,supply curve of Covid vaccine |
| JEL: | C73 D03 D43 C72 D81 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esrepo:227776&r=all |
| By: | Elisenda Molina; Juan Tejada; Tom Weiss |
| Abstract: | In this paper, we propose and analyse two game theoretical models useful to design marketing channels attribution mechanisms based on cooperative TU games and bankruptcy problems, respectively. First, we analyse the Sum Game, a coalitional game introduced by Morales (2016). We extend the ideas introduced in Zhao et al. (2018) and Cano-Berlanga et al. (2017) to the case in which the order and the repetition of channels on the paths to conversion are taken into account. In all studied cases, the Shapley value is proposed as the attribution mechanism. Second, a bankruptcy problem approach is proposed, and a similar analysis is developed relying on the Constrained Equal Loss (CEL) and Proportional (PROP) rules as attribution mechanisms. In particular, it is relevant to note that the class of attribution bankruptcy problems is a proper subclass of bankruptcy problems. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.00812&r=all |
| By: | Emmanuel LORENZON |
| Abstract: | We consider a private value auction with one-sided incomplete information in which two objects are sold in a sequence of two second-price auctions. Buyers have multi-unit demands and both are asymmetrically informed at the ex-ante stage of the game. One buyer perfectly knows his type and the other is uninformed about his own type. We con-sider interim information acquisition for the uninformed buyer and derive an asymmetric equilibrium which is shown to produce a declining price sequence across both sales. The supermartingale property of the price sequence stems from the uninformed buyer’s incen-tives to gather private information which leads to an aggressive bidding at the first-stage auction. |
| Keywords: | Sequential auctions; Uninformed bidding; Multi-unit demand; Declining price anomaly |
| JEL: | D44 D82 L86 M37 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:grt:bdxewp:2020-20&r=all |
| By: | Manfred J. Holler (University of Hamburg and CCR-Munich); Florian Rupp (Technical University Munich and CCR-Munich) |
| Abstract: | This paper analyzes a network constituency which is characterized by voting in a political network. It applies power index analysis to the notorious Krackhardt’s kite social network by imposing a weighted voting game on the given network structure. It compares the results of this analysis, derived by applying the Public Good Index and the Public Value, with the outcome of employing the centrality concepts - degree centrality, closeness centrality, and betweenness centrality - that we find in Krackstadt (1990), and eigenvector centrality. Alternative collective decision rules and alternative network structure are considered. The study is concurs with a real-world collective decision problem which one of the authors experiences concerning a massive expansion of housebuilding with the City of Munich, the State of Bavaria and some German Federal Government institutions as possible players in a decision network. Other players are the Nature and Biodiversity Conservation Union, the farmers who are threatened by the expropriation of land and the incumbent inhabitants of the area who like their last resort of green fields and relatively fresh air, and already suffer from the heavy traffic in this area. The city’s housebuilding project is strongly contested. |
| Keywords: | network, centrality, Public Good Index, Public Value, power indices, weighted voting game, collective decision rules |
| JEL: | C70 C72 D72 D85 L14 Z13 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cccrwp:2019-07-ccr&r=all |
| By: | Andrew Kosenko |
| Abstract: | We study a game of strategic information design between a sender, who chooses state-dependent information structures, a mediator who can then garble the signals generated from these structures, and a receiver who takes an action after observing the signal generated by the first two players. We characterize sufficient conditions for information revelation, compare outcomes with and without a mediator and provide comparative statics with regard to the preferences of the sender and the mediator. We also provide novel conceptual and computational insights about the set of feasible posterior beliefs that the sender can induce, and use these results to obtain insights about equilibrium outcomes. The sender never benefits from mediation, while the receiver might. The receiver benefits when the mediator's preferences are not perfectly aligned with hers; rather the mediator should prefer more information revelation than the sender, but less than perfect |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.00098&r=all |
| By: | Florian Engl |
| Abstract: | This paper studies experimentally when and how ideological motives shape outcomes in group decision-making scenarios. Groups play a repeated coordination game in which they can agree on a payoff-dominant or a payoff-dominated but ideologically preferred outcome, or disagree and forego all payoffs. We find that groups which disagree initially are more likely to end up agreeing on the ideologically preferred outcome. We classify subjects into ideologically motivated and payoff motivated types and show that this effect stems from the two types’ differential reaction to disagreements. After disagreements, ideologically motivated types are more committed and steer the group towards their preferred outcome. Heterogeneous groups disagree more often and, thus, foster agreements on the ideologically motivated outcome. Our treatments show that, because of this mechanism, large groups are more likely to implement the ideologically preferred outcome than small groups. Furthermore, we show that individual ideological commitment is stronger when it targets the prevention of an outcome in conflict with the ideology than when it targets the implementation of an outcome aligned with the ideology. Theoretically, we study whether fixed or malleable ideological preferences can explain our results. |
| Keywords: | ideology, group decision-making, coordination, heterogeneous types |
| JEL: | C92 D01 D70 D91 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8742&r=all |
| By: | Xianwen Shi; Jun Zhang |
| Abstract: | We study welfare consequences of third-degree price discrimination and market segmentation in a duopoly market with captive and contested consumers. A market segmentation divides the market into segments that contain different proportions of captive and contested consumers. Firm-optimal segmentation divides the market into two segments and in each segment only one firm has captive consumers. In contrast to the existing literature with exogenous segmentation, price discrimination under firm-optimal segmentation unambiguously reduces consumer surplus for all markets. Consumer-optimal segmentation divides the market into a maximal symmetric segment and the remainder, and yields the lowest producer surplus among all segmentations. |
| Keywords: | Price Discrimination, Market Segmentation, Information Design, Welfare |
| JEL: | D43 D82 |
| Date: | 2020–12–25 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-682&r=all |
| By: | Wolfgang Buchholz; Dirk Rübbelke |
| Abstract: | It is explored in this paper how – depending on the agents’ preferences – an unequal income distribution may lead to a higher public good supply in a non-cooperative Nash equilibrium than in a cooperative Lindahl equilibrium that arises from a balanced income distribution. The degree of inequality that is needed for producing this result may be moderate what in particular is shown through an example with CES preferences. |
| Keywords: | public good, Nash equilibrium, Lindahl equilibrium, income distribution |
| JEL: | D31 H41 Q54 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8786&r=all |
| By: | Alessandra Casella; Evan Friedman; Manuel Perez Archila |
| Abstract: | Mechanism design teaches us that a mediator can strictly improve the chances of peace between two opponents even when the mediator has no independent resources, is less informed than the two parties, and has no enforcement power. We test the theory in a lab experiment where two subjects negotiate how to share a resource; in case of conflict, the subjects' privately known strength determines their payoffs. The subjects send cheap talk messages about their strength to one another (in the treatment with direct communication) or to the mediator (in the mediation treatment), before making their demands or receiving the mediator's recommendations. We find that, in line with the theory, messages are significantly more sincere when sent to the mediator. However, contrary to the theory, peaceful resolution is not more frequent, even when the mediator is a computer implementing the optimal mediation program. While the theoretical result refers to the best (i.e. most peaceful) equilibrium under mediation, multiple equilibria exist, and the best equilibrium is particularly vulnerable to small deviations from full truthfulness. Subjects are not erratic and their deviations induce only small losses in payoffs, and yet they translate into significant increases in conflict. |
| JEL: | C78 C92 D74 D82 D86 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:28137&r=all |
| By: | Lea Heursen; Eva Ranehill; Roberto A. Weber |
| Abstract: | We study whether one reason behind female underrepresentation in leadership is that female leaders are less effective at coordinating action by followers. Two experiments using coordination games investigate whether female leaders are less successful than males in persuading followers to coordinate on efficient equilibria. Group performance hinges on higher-order beliefs about the leader’s capacity to convince followers to pursue desired actions, making beliefs that women are less effective leaders potentially self-confirming. We find no evidence that such bias impacts actual leadership performance, identifying a precisely-estimated null effect. We show that this absence of an effect is surprising given experts’ priors. |
| Keywords: | gender, coordination games, leadership, experiment |
| JEL: | D23 C72 C92 J10 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8713&r=all |
| By: | Yasuyuki Miyahara (Kobe University); Hitoshi Sadakane (Kyoto University) |
| Abstract: | We analyze a situation in which an uninformed decision maker can gather information about states by paying a cost before communicating with an informed sender. We focus on multidimensional information gathering: the decision maker can determine how much time to allocate to gather information about each state. It is shown that communication can be enhanced under multidimensional information gathering compared with no information gathering. We also characterize the optimal investigation, which specifies the state the decision maker gathers information about. Our result demonstrates an advantage of multidimensional information gathering over single-dimensional information gathering. |
| Keywords: | Cheap talk; Communication; Multidimensional information gathering; Strategic information transmission Technology choice; CES production function |
| JEL: | C72 C73 D83 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:1050&r=all |
| By: | Mabrouk, R.; Kurtyka, O. |
| Abstract: | We analyze firms' choice of abatement technology in vertical chains. A downstream polluting monopoly can buy a license from an upstream supplier with mature end-of-pipe equipment (outsider) or develop an in-house clean technology. Insiders innovation may be undertaken only to increase bargaining power of the polluter. We put the light on the strategic role of environmental regulation to influence this choice. We find that the role of regulator as a technology forcing authority is confirmed in regions of under-investment. However, under certain conditions, an over-investment occurs that forces the regulator to become laxer. Paradoxically, the regulator may oppose innovation even if the resulting technology is used by the innovator. All these results rely upon the creation of total profits from the integrated vertical structure. |
| Keywords: | ENVIRONMENTAL INNOVATION;ABATEMENT TECHNOLOGY;CLEAN TECHNOLOGY;END-OF-PIPE EQUIPMENT;VERTICAL CHAIN;REGULATION;BARGAINING |
| JEL: | D43 H23 L13 Q42 Q58 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:gbl:wpaper:2020-13&r=all |
| By: | Wang Zhijian; Yao Qingmei |
| Abstract: | Nash equilibrium, its reality and accuracy, is firstly illustrated by the O'Neill (1987) game experiment. In this game experiments (O'Neill (1987), Binmore (2001) and Okano (2013)), we discover the fine structure in the human social cycling spectrum. With the eigencycle set from the eigenvectors in game dynamics equations, we can have the accuracy increased by an order of magnitude on the dynamics testing. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.03315&r=all |
| By: | Tim Roughgarden |
| Abstract: | EIP-1559 is a proposal to make several tightly coupled additions to Ethereum's transaction fee mechanism, including variable-size blocks and a burned base fee that rises and falls with demand. This report assesses the game-theoretic strengths and weaknesses of the proposal and explores some alternative designs. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.00854&r=all |
| By: | Hitoshi Matsushima (University of Tokyo) |
| Abstract: | We investigate the unique implementation problem of social choice functions (SCFs) from ethical and epistemological concerns. According to Matsushima and Noda (2020), we consider the possibility that in higher-order beliefs there exists an agent who is honest, that is, motivated by intrinsic preference for honesty as well as material interest. We assume only weak honesty in that an honest agent is mostly motivated by material interests and even tells a white lie. We show a very permissive result that any social choice function is uniquely implementable in Bayes Nash equilibrium if “all agents are selfish†never happens to be common knowledge. Hence, any SCF is uniquely implementable even if all agents are selfish and “all agents are selfish†is mutual knowledge. Importantly, any ethical SCF is uniquely implementable whenever “all agents are selfish†never happens to be common knowledge while it is never uniquely implementable otherwise. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf500&r=all |