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on Game Theory |
| By: | Frank Huettner (ESMT Berlin); André Casajus (HHL Leipzig Graduate School of Management) |
| Abstract: | In the absence of externalities, marginality is equivalent to an independence property that rests on Harsanyi‘s dividends. These dividends identify the surplus inherent to each coalition. Independence states that a player‘s payoff stays the same if only dividends of coalitions to which this player does not belong to change. We introduce notions of marginality and independence for games with externalities. We measure a player‘s contribution in an embedded coalition by the change in the worth of this coalition that results when the player is removed from the game. We provide a characterization result using efficiency, anonymity, and marginality or independence, which generalizes Young‘s characterization of the Shapley value. An application of our result yields a new characterization of the solution put forth by Macho-Stadler et al. (J Econ Theor, 135, 2007, 339-356) without linearity, as well as for almost all generalizations put forth in the literature. The introduced method also allows us to investigate egalitarian solutions and to reveal how accounting for externalities may result in a deviation from the Shapley value. This is exemplified with a new solution that is designed in a way to not reward external effects, while at the same time it cannot be assumed that any partition is the default partition. |
| Keywords: | Shapley value, potential, restriction operator, partition function form game, externalities |
| JEL: | C71 D60 |
| Date: | 2019–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:esm:wpaper:esmt-19-01&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of bidders’ independent signals. If the object is optimally sold with probability one, then the optimal mechanism is simply a posted price, with the highest price such that every type of every bidder is willing to buy the object. A sufficient condition for the posted price to be optimal among all mechanisms is that there is at least one potential bidder who is omitted from the auction. If the object is optimally sold with probability less than one, then optimal mechanisms skew the allocation towards bidders with lower signals. This can be implemented via a modi?ed Vickrey auction, where there is a random reserve price for just the high bidder. The resulting allocation induces a “winner’s blessing,” whereby the expected value conditional on winning is higher than the unconditional expectation. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the ?rst-price, second-price or English auctions) deliver lower revenue because of the winner’s curse generated by the allocation rule. Our qualitative results extend to more general common value environments where the winner’s curse is large. |
| Keywords: | Optimal auction, Common values, Maximum game, Posted price, Reserve price, Revenue equivalence |
| JEL: | C72 D44 D82 D83 |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2147r&r=all |
| By: | Astrid Dannenberg (University of Kassel); Carlo Gallier (Leibniz Centre for European Economic Research) |
| Abstract: | A growing experimental literature studies the endogenous choice of institutions to solve cooperation problems arising in prisoners’ dilemmas, public goods games, and common pool resource games. Participants in these experiments have the opportunity to influence the rules of the game before they play the game. In this paper, we review the experimental literature of the last 20 years on the choice of institutions and describe what has been learned about the quality and the determinants of institutional choice. Almost all institutions improve cooperation if they are implemented, but they are not always implemented by the players. Institutional costs, remaining free-riding incentives, and a lack of learning opportunities are the most important barriers. At the individual level, own cooperativeness and beliefs about other players’ behavior can be identified as important determinants of institutional choice. Cooperation tends to be higher under endogenously chosen institutions than exogenously imposed institutions. However, a significant share of players fails to implement the institution and they often perform poorly, which is why we cannot conclude that letting people choose is better than enforcing institutions from outside. |
| Keywords: | Literature review; experiments; cooperation; public goods; endogenous institutional choice; voting |
| JEL: | C71 C91 C92 D02 D70 H41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:mar:magkse:201911&r=all |
| By: | Gaudeul, Alexia; Keser, Claudia; Müller, Stephan |
| Abstract: | We study the coexistence of strategies in the indirect reciprocity game where agents have access to second-order information. We fully characterize the evolutionary stable equilibria and analyze their comparative statics with respect to the cost-benefit ratio (CBR). There are indeed only two stable sets of equilibria enabling cooperation, one for low CBRs involving two strategies and one for higher CBR's which involves two additional strategies. We thereby offer an explanation for the coexistence of different moral judgments among humans. Both equilibria require the presence of second-order discriminators which highlights the necessity for higher-order information to sustain cooperation through indirect reciprocity. In a laboratory experiment, we find that more than 75% of subjects play strategies that belong to the predicted equilibrium set. Furthermore, varying the CBR across treatments leads to changes in the distribution of strategies that are in line with theoretical predictions. |
| Keywords: | Indirect reciprocity,Cooperation,Evolution,Experiment |
| JEL: | C73 C91 D83 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cegedp:370&r=all |
| By: | Christian Bontemps (ENAC - Ecole Nationale de l'Aviation Civile); Rohit Kumar |
| Abstract: | In this paper, we consider inference procedures for entry games with complete information. Due to the presence of multiple equilibria, we know that such a model may be set-identified without imposing further restrictions. We complete the model with the unknown selection mechanism and characterize geometrically the set of predicted choice probabilities, in our case, a convex polytope with many facets. Testing whether a parameter belongs to the identified set is equivalent to testing whether the true choice probability vector belongs to this convex set. Using tools from the convex analysis, we calculate the support function and the extreme points. The calculation yields a finite number of inequalities, when the explanatory variables are discrete, and we characterized them once for all. We also propose a procedure that selects the moment inequalities without having to evaluate all of them. This procedure is computationally feasible for any number of players and is based on the geometry of the set. Furthermore, we exploit the specific structure of the test statistic used to test whether a point belongs to a convex set to propose the calculation of critical values that are computed once and independent of the value of the parameter tested, which drastically improves the calculation time. Simulations in a separate section suggest that our procedure performs well compared with existing methods. |
| Keywords: | support function,entry games,convex set,set-identification |
| Date: | 2019–05–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02137356&r=all |
| By: | Patrice Cassagnard (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour); Pierre Regibeau (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour) |
| Abstract: | We propose a simple two-stages duopoly game where two firms produce an homogeneous good to satisfy the demand in a foreign market. First they decide whether to serve this market with exports or with foreign direct investments and then they play a one-shot Cournot-Nash game. This game has been made even more complex by the fact that foreign direct investments induce technological spillovers which imply the possible entry of a third firm. From the complete characterization of the equilibria we show that a small disadvantage of one of the both firms can conduce this firm to invest alone in the foreign country rather than export. In this case, the investment is motivated by the fact that the dissipation risk of both firm-specific assets to a local potential entrant -triopoly payoffs- is beared by the two firms whereas the gain -increased market share in duopoly- is captured by the firm which chooses to invest abroad. We have in mind the competition between Airbus and Boeing in China. |
| Keywords: | Entry Deterrence,FDI,Export,Cournot duopoly,Spillovers,Airbus and Boeing |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02141056&r=all |
| By: | Zhonghao Shui (Graduate School of Economics, Kyoto University) |
| Abstract: | This paper considers an auctioneer who has a non-monotonic utility function with a unique maximizer. The auctioneer is able to reject all bids over some amount by using rejection prices. We show that the optimal rejection price for such an auctioneer is lower than and equal to that maximizer in first-price and second-price sealed-bid auctions, respectively. Further, in each auction we characterize a necessary and sufficient condition that by using the optimal rejection price not only the auctioneer but also bidders can be better off, compared to a standard auction. Finally, we find that the auctioneer strictly prefers a first-price sealed-bid auction if he is risk-averse when his revenue is lower than the maximizer or if the distribution of revenues which are lower than the maximizer in a standard first-price sealed-bid auction is first-order stochastic dominant over the one in a standard second-price sealed-bid auction. |
| Keywords: | Auction, Rejection prices, Non-monotonic utility |
| JEL: | D44 D82 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:1008&r=all |
| By: | Joyee Deb; Aniko Oery; Kevin R. Williams |
| Abstract: | We study reward-based crowdfunding campaigns, a new class of dynamic contribution games where consumption is exclusive. Two types of backers participate: buyers want to consume the product while donors just want the campaign to succeed. The key tension is one of coordination between buyers, instead of free-riding. Donors can alleviate this coordination risk. We analyze a dynamic model of crowdfunding and demonstrate that its predictions are consistent with high-frequency data collected from Kickstarter. We compare the Kickstarter mechanism to alternative platform designs and evaluate the value of dynamically arriving information. We extend the model to incorporate social learning about quality. |
| JEL: | D21 D22 D7 D8 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25881&r=all |
| By: | Patrick Lahr; Justus Winkelmann |
| Abstract: | We consider a multi-sender cheap talk model, where the receiver faces uncertainty over whether senders have aligned or state-independent preferences. This uncertainty generates a trade-off between giving sufficient weight to the most informed aligned senders and minimizing the influence of the unaligned. We show that preference uncertainty diminishes the benefits from specialization, i.e., senders receiving signals with more dispersed accuracy. When preference uncertainty becomes large, it negates them entirely, causing qualified majority voting to become the optimal form of communication. Our results demonstrate how political polarization endangers the ability of society to reap the benefits of specialization in knowledge. |
| Keywords: | Cheap Talk, Information Aggregation, Voting |
| JEL: | D83 D71 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_093&r=all |
| By: | Simon P. Anderson; Martin Peitz |
| Abstract: | We customize the aggregative game approach to oligopoly to study media platforms which may differ by popularity. Advertiser, platform, and consumer surplus are tied together by a simple summary statistic. When media are ad-financed and ads are a nuisance to consumers we establish see-saws between consumers and advertisers. Entry increases consumer surplus, but decreases advertiser surplus if industry platform profits decrease with entry. Merger decreases consumer surplus, but advertiser surplus tends to increase. By contrast, when platforms use two-sided pricing or consumers like advertising, advertiser and consumer interests are often aligned. |
| Keywords: | media economics, mergers, entry, advertising, aggregative games |
| JEL: | D43 L13 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_089&r=all |