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on Game Theory |
| By: | Anne-Christine Barthel (West Texas A&M University West Texas A&M University Canyon, TX, 79016, USA); Eric Hoffmann (West Texas A&M University West Texas A&M University Canyon, TX, 79016, USA); Tarun Sabarwal (Department of Economics, University of Kansas) |
| Abstract: | In game theory, p-dominance and p-best response sets serve as important robustness solution concepts by allowing for deviations from the stringent common knowledge requirements of Nash equilibrium. However, solving for such sets remains largely intractable beyond the simplest of settings. The contributions of this paper are twofold: First, in monotone games, (which include the broad class of supermodular games, submodular games, and their combinations,) we show that these concepts can be characterized in terms of pure strategy Nash equilibria in an auxiliary game of complete information. This makes it considerably easier to compute such sets, facilitating their broader use. Second, these characterizations lead to new results about the structure of entire classes of such solution concepts, including minimal p-best response (p-MBR) sets, which generalize wellknown results for pure strategy Nash equilibria. In games with strategic complements, these classes are complete lattices. More generally, they are totally unordered. Several examples highlight the results. |
| Keywords: | Strategic complements, Strategic substitutes, Monotone games, p-dominance, p-best response set |
| JEL: | C60 C70 C72 |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202012&r=all |
| By: | Jin Yeub Kim (Yonsei Univ) |
| Abstract: | This paper studies Myerson's neutral bargaining solution for a class of Bayesian bargaining problems in which the solution is unique. For this class of examples, I consider a noncooperative mechanism-selection game. I find that all of the interim incentive efficient mechanisms can be supported as sequential equilibria. Further, standard refinement concepts and selection criteria do not restrict the large set of interim Pareto-undominated sequential equilibria. I provide a noncooperative foundation of the neutral bargaining solution by characterizing the solution as a unique coherent equilibrium allocation. |
| Keywords: | Neutral bargaining solution, mechanism-selection game, equilibrium refinement, equilibrium selection criterion, credibility, coherent plan |
| JEL: | C71 C72 C78 D82 |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2020rwp-175&r=all |
| By: | Giorgio Fabbri (Univ. Grenoble Alpes, CNRS, France); Silvia Faggian (Department of Economics, Ca’ Foscari University of Venice, Italy); Giuseppe Freni (Department of Business and Economics, Parthenope University of Naples, Italy) |
| Abstract: | We study the dynamics of the exploitation of a natural resource, distributed in space and mobile, where spatial diversification is introduced by a network structure. Players are assigned to different nodes by a regulator, after he/she decides at which nodes natural reserves are established. The game solution shows how the dynamics of spatial distribution depends on the productivity of the various sites, on the structure of the connections between the various locations, and on the preferences of the agents. At the same time, the best locations to host a nature reserve are identified in terms of the parameters of the model, and it turns out they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network which takes into account the nodes productivities. |
| Keywords: | Harvesting, spatial models, differential games, nature reserve |
| JEL: | Q20 Q28 R11 C73 |
| Date: | 2020–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvir:2020022&r=all |
| By: | Satoru Fujishige; Zaifu Yang |
| Abstract: | We propose a new and general dynamic design for efficiently auctioning multiple heterogeneous indivisible items. The auction applies to all unimodular demand types of Baldwin and Klemperer (2019) which are a necessary and sufficient condition for the existence of competitive equilibrium in economies with indivisible goods and accommodate a variety of substitutes, complements, gross substitutes and complements, strong substitutes, and other kinds. Every bidder has private valuation on each of his interested bundles of items and the seller has a reserve price for every bundle of items. The auctioneer announces the current prices for all items, bidders respond by reporting their demands at these prices, and then the auctioneer adjusts the prices of items. The trading rules are simple, transparent, and detail-free. Although bidders are not assumed to be price-takers so they can strategically exercise their market power, this auction induces bidders to bid truthfully and yields an efficient outcome. Bidding sincerely is an ex post perfect Nash equilibrium. The auction is also privacy-preserving and independent of any probability distribution assumption. |
| Keywords: | Dynamic Auction, Incentive-Compatibility, Competitive Equilibrium, Unimodular Demand Types, Substitute, Complement, Indivisibility, Dynamic Auction Game of Incomplete Information. |
| JEL: | D44 C78 |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:20/08&r=all |
| By: | Jin Yeub Kim (Yonsei Univ) |
| Abstract: | I consider two-person bargaining problems in which mechanism is selected at the almost ex ante stage-when there is some positive probability that players may have learned their private types-and the chosen mechanism is implemented at the interim stage. For these problems, I define almost ex ante incentive efficient mechanisms and apply the concept of neutral optima (Myerson 1984b). I show that those mechanisms may not be ex ante incentive efficient. This note suggests that ex ante incentive efficient mechanisms are not robust to a perturbation of the ex ante informational structure at the time of mechanism selection. |
| Keywords: | Bargaining; Incomplete information; Mechanism selection; Almost ex ante stage; Incentive efficiency; Neutral optima |
| JEL: | C71 C78 D74 D82 |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2020rwp-174&r=all |
| By: | Antonio J. Morales (Universidad de Málaga); Ismael Rodriguez-Lara (Universidad de Granada; Economic Science Institute, Chapman University) |
| Abstract: | Testing causal relationships expressed by mathematical models on facts about human behaviour across history is challenging. A prominent example is the Neolithic agricultural revolution [1]. Many theoretical models of the adoption of agriculture has been put forward [2] but none has been tested. The only exception is [3], that uses a computational approach with agent-based simulations of evolutionary games. Here, we propose two games that resemble the conditions of human societies before and after the agricultural revolution. The agricultural revolution is modelled as an exogenous shock in the lab (n=180, 60 independent groups), and the transition from foraging to farming results from an equilibrium selection process decided by experimental subjects. The experimental data replicate the known facts that foragers organized themselves around division of labour [4] and were more egalitarian than farmers [5]. There is also evidence of bi-modal distribution along the foraging-farming axis with many in-between groups [6, 7, 8]. These results provide direct evidence that the modes of production determine the system of values of societies (inequality) and lend support for the idea that human moved in a widespread manner from foraging to farming societies. We also find that cultural and institutional preconditions were crucial for farming [9], as more egalitarian foraging groups adopted earlier agricultural techniques, but inequality raises in farming societies as agriculture settles [10], with the long run success of agriculture being determined by the land-owner’s legitimacy. These results enrich our understanding of the Neolithic agricultural revolution and highlight the relevance of experimental methodology to generate a rich dataset that complements the fragmented evidence from archaeological sites. |
| Keywords: | Inequality; Agricultural Revolution; Foragers Societies; Farming Societies; Property Rights; Land-owner; Human Values; Experimental Economics |
| JEL: | C72 C92 D02 D31 D70 N00 N50 O33 P14 Z13 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-20&r=all |
| By: | Alessandro Sontuoso (Smith Institute for Political Economy and Philosophy, Chapman University; Center for Social Norms and Behavioral Dynamics, University of Pennsylvania); Christina Bicchieri (Center for Social Norms and Behavioral Dynamics, University of Pennsylvania); Alexander Funcke (Center for Social Norms and Behavioral Dynamics, University of Pennsylvania); Einav Hart (Center for Social Norms and Behavioral Dynamics, University of Pennsylvania) |
| Abstract: | We study games where the impact of strategic uncertainty (i.e., ambiguity arising from uncertainty about other players’ actions and beliefs) is compounded by the simultaneous presence of risky prospects (chance moves with commonly-known conditional probabilities). We embed such games in an experimental environment that allows us to test if risk-taking behavior is affected by information that reduces the extent of strategic uncertainty. In doing so, we test some implications of expected utility theory, while making minimal assumptions about individual-level (risk or ambiguity) attitudes. Our analysis provides evidence for an effect of the information: notably, we find that the effect on choice behavior is triggered in some cases by a rational belief revision about others’ actions, and in other cases by a reversal in risk preferences. |
| Keywords: | Strategic Uncertainty; Risk Preferences; Belief Revision; Mixed-Motive games; Network |
| JEL: | C72 C92 D81 D83 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-23&r=all |
| By: | Lukasz Balbus; Pawel Dziewulski; Kevin Reffett; Lukasz Wozny |
| Abstract: | We present a new approach for studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Distributional Equilibrium (MSDE), prove its existence, and provideconstructive methods for characterizing and comparing equilibrium distributional transitional dynamics. To analyze equilibrium transitions for the distributions ofprivate types, we develop an appropriate dynamic (exact) law of large numbers.Finally, we show that our models can be approximated as idealized limits of gameswith a large (but finite) number of players. We provide numerous applications of theresults including: dynamic models of growth with status concerns, social distance and paternalistic bequest with endogenous preference for consumption. |
| Keywords: | large games, distributional equilibria, supermodular games, compara-tive dynamics, non-aggregative games, law of large numbers, social interactions |
| JEL: | C62 C72 C73 |
| Date: | 2020–07 |
| URL: | http://d.repec.org/n?u=RePEc:sgh:kaewps:2020052&r=all |
| By: | László Á. Kóczy (Institute of Economics, Centre for Economic and Regional Studies, Tóth Kálmán u. 4., H-1097 Budapest, Hungary and Department of Finance, Faculty of Economic and Social Sciences, Budapest University of Technology and Economics, Magyar tudósok körútja 2., H-1111 Budapest, Hungary) |
| Abstract: | The Covid-19 epidemic highlighted the significance of externalities: contacts with other people do not only affect our chances of getting infected but also our entire network.We introduce a model for coalitional network stability in networks with widespread externalities. The network function form generalises the partition function form of cooperative games in allowing the network structure to be taken into account. The recursive core for network function form games generalises the recursive core for such environments and its properties also rhyme with the corresponding inclusion properties of the optimistic and pessimistic recursive cores and can be seen as a modification of pairwise stability to a coalitional setting where the involvement of more players allows for the -- partial -- internalisation of the externalities, but we also allow residual players to endogenously respond to any externalities that may affect them. We present two simple examples to illustrate positive and negative externaliti.The first is of a favour network and show that the core is nonempty when players must pay transfers to intermediaries; this simple setting also models economic situations such as airline networks. The second models social contacts during an epidemic and finds social bubbles as the solution. |
| Keywords: | externalities, networks, recursive core, social bubble |
| JEL: | C71 C72 |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2026&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Philipp Strack (Cowles Foundation, Yale University) |
| Abstract: | A single seller faces a sequence of buyers with unit demand. The buyers are forwardlooking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the buyer decides to participate in the mechanism. The resulting value function of each buyer cannot be too convex and must be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each buyer: he participates either immediately or at a future random time. |
| Keywords: | Dynamic Mechanism Design, Observable Arrival, Unobservable Arrival, Repeated Sales, Interim Incentive Constraints, Interim Participation Constraints, Stopping Problem, Option Value, Progressive Participation |
| JEL: | D44 D82 D83 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2189r2&r=all |
| By: | Ernesto Mesa-Vázquez (University of Valencia & ERICES.); Ismael Rodriguez-Lara (Department of Economic Theory and Economic History, University of Granada.); Amparo Urbano (University of Valencia & ERICES.) |
| Abstract: | Using a multiple-price list dictator game, this paper provides experimental evidence that the level of generosity is affected when we vary the probability that the dictator’s decision will be implemented. We also show that framing matters for generosity in that subjects are less generous when their choices under role uncertainty are such that subjects perceive that they are in the role of dictators and know that their choices will be implemented with a certain probability, compared with a setting in which subjects are told that they are in the role of recipients and know that their choices will not be implemented with certain probability. |
| Keywords: | dictator games, generosity, role uncertainty, framing effects. |
| JEL: | C91 D3 D6 D81 |
| Date: | 2019–07–29 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:20/05&r=all |
| By: | Mikhail Anufriev (University of Technology Sydney); John Duffy (University of California); Valentyn Panchenko (UNSW Business School) |
| Abstract: | We introduce a planar beauty contest game where agents must simultaneously guess two, endogenously determined variables, a and b. The system of equations determining the actual values of a and b is a coupled system; while the realization of a depends on the average forecast for a, a, as in a standard beauty contest game, the realization of b depends on both a and on the average forecast for b, b. Our aim is to better understand the conditions under which agents learn the steady state of such systems and whether the eigenvalues of the system matter for the convergence or divergence of this learning process. We find that agents are able to learn the steady state of the system when the eigen- values are both less than 1 in absolute value (the sink property) or when the steady state is saddle path stable with the one root outside the unit circle being negative. By contrast, when the steady state exhibits the source property (two unstable roots) or is saddle path stable with the one root outside the unit circle being positive, subjects are unable to learn the steady state of the system. We show that these results can be explained by either an adaptive learning model or a mixed cognitive levels model, while other approaches, e.g., na•ve or homo-geneous level-k learning, do not consistently predict whether subjects converge to or diverge away from the steady state. |
| Keywords: | Beauty Contest; Learning; Stability; Simultaneous Equation Systems, Level-k cognitive theory |
| JEL: | C30 C92 D83 D84 |
| Date: | 2019–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:2019/10&r=all |
| By: | Grossman, Gene M.; Helpman, Elhanan |
| Abstract: | Misinformation pervades political competition. We introduce opportunities for political can- didates and their media supporters to spread fake news about the policy environment and perhaps about parties'positions into a familiar model of electoral competition. In the baseline model with full information, the parties'positions converge to those that maximize aggregate welfare. When parties can broadcast fake news to audiences that disproportionately include their partisans, policy divergence and suboptimal outcomes can result. We study a sequence of models that impose progressively tighter constraints on false reporting and characterize situa- tions that lead to divergence and a polarized electorate. |
| Keywords: | Electoral Competition; fake news; policy positions |
| JEL: | D78 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:14210&r=all |
| By: | Yanlin Chen (Nanjing Audit University); Jun Zhang (University of Technology Sydney) |
| Abstract: | This paper investigates how a privately informed seller could signal her type through Bayesian persuasion and pricing strategy. We find that it is generally impossible to achieve separation through one channel alone. Furthermore, the outcome that survives the intuitive criterion always exists and is unique. This outcome is separating, for which a closed-form solution is provided. The signaling concern forces the high-type seller to disclose inefficiently more information and charge a higher price, resulting in fewer sales and lower profit. Finally, we show that a regulation on minimal quality could potentially hurt social welfare, and private information hurts the seller. |
| Keywords: | Bayesian persuasion; signaling; information disclosure; informed principal |
| JEL: | D82 D83 L12 |
| Date: | 2019–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:2019/14&r=all |
| By: | Armstrong, Mark; Zhou, Jidong |
| Abstract: | This paper studies competition between firms when consumers observe a private signal of their preferences over products. Within the class of signal structures which allow pure-strategy pricing equilibria, we derive signal structures which are optimal for firms and those which are optimal for consumers. The firm-optimal signal structure amplifies the underlying product differentiation, thereby relaxing competition, while ensuring that consumers purchase their preferred product, thereby maximizing total welfare. The consumer-optimal structure dampens differentiation, which intensifies competition, but induces some consumers with weak preferences between products to buy their less-preferred product. The analysis sheds light on the limits to competition when the information possessed by consumers can be designed flexibly. |
| Keywords: | Bertrand Competition; information design; Online platforms; product differentiation |
| JEL: | D43 D47 D83 L13 L15 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:14162&r=all |