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on Game Theory |
| By: | J\'anos Flesch; Arkadi Predtetchinski; Ville Suomala |
| Abstract: | The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the tree. The payoff in a game is defined as the infimum of the capacity over the nodes that have been visited during the play. The active player, the number of children, and the capacity are drawn from a given joint distribution independently across the nodes. We characterize the cumulative distribution function of the value $v$ using the fixed points of the so-called value generating function. The characterization leads to a necessary and sufficient condition for the event $v \geq k$ to occur with positive probability. We also study probabilistic properties of the set of Player I's $k$-optimal strategies and the corresponding plays. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.10528&r= |
| By: | Vasily V. Gusev (National Research University Higher School of Economics) |
| Abstract: | This paper studies a model for cooperative congestion games. There is an array of cooperative games V and a player’s strategy is to choose a subset of the set V. The player gets a certain payoff from each chosen game. The paper demonstrates that if a payoff is the Shapley or the Banzhaf value, then the corresponding cooperative congestion game has a Nash equilibrium in pure strategies. The case is examined where each game in V has a coalition partition. The stability of the vector of coalition structures is determined, taking in to account the transitions of players with in a game and their migrations to other games. The potential function is defined for coalition partitions, and is used as a means of proving the existence of a stable vector of coalition structures for a certain class of cooperative game values. |
| Keywords: | potential games, Nash stability, coalition structure, congestion games |
| JEL: | C60 C62 C71 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:245/ec/2021&r= |
| By: | Iwan Bos (Department of Organisation, Strategy and Entrepreneurship, Maastricht University); Marco A. Marini (Department of Social Sciences and Economics, Sapienza University of Rome); Riccardo D. Saulle (Department of Economics and Management, University of Padova) |
| Abstract: | This paper examines capacity-constrained oligopoly pricing with sellers who seek myopic improvements. We employ the Myopic Stable Set stability concept and establish the existence of a unique pure-strategy price solution for any given level of capacity. This solution is shown to coincide with the set of pure-strategy Nash equilibria when capacities are large or small. For an intermediate range of capacities, it predicts a price interval that includes the mixed-strategy support. This stability concept thus encompasses all Nash equilibria and offers a pure-strategy solution when there is none in Nash terms. In particular, it provides a behavioral rationale for different types of pricing dynamics, including real-world economic phenomena such as Edgeworth-like price cycles, price dispersion and supply shortages. |
| Keywords: | Behavioral IO, Bounded Rationality, Capacity Constraints, Oligopoly Pricing, Myopic Stable Set. |
| JEL: | C72 D43 L13 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:saq:wpaper:5/21&r=all |
| By: | Michael Foley; Rory Smead; Patrick Forber; Christoph Riedl |
| Abstract: | Can egalitarian norms or conventions survive the presence of dominant individuals who are ensured of victory in conflicts? We investigate the interaction of power asymmetry and partner choice in games of conflict over a contested resource. We introduce three models to study the emergence and resilience of cooperation among unequals when interaction is random, when individuals can choose their partners, and where power asymmetries dynamically depend on accumulated payoffs. We find that the ability to avoid bullies with higher competitive ability afforded by partner choice mostly restores cooperative conventions and that the competitive hierarchy never forms. Partner choice counteracts the hyper dominance of bullies who are isolated in the network and eliminates the need for others to coordinate in a coalition. When competitive ability dynamically depends on cumulative payoffs, complex cycles of coupled network-strategy-rank changes emerge. Effective collaborators gain popularity (and thus power), adopt aggressive behavior, get isolated, and ultimately lose power. Neither the network nor behavior converge to a stable equilibrium. Despite the instability of power dynamics, the cooperative convention in the population remains stable overall and long-term inequality is completely eliminated. The interaction between partner choice and dynamic power asymmetry is crucial for these results: without partner choice, bullies cannot be isolated, and without dynamic power asymmetry, bullies do not lose their power even when isolated. We analytically identify a single critical point that marks a phase transition in all three iterations of our models. This critical point is where the first individual breaks from the convention and cycles start to emerge. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.08636&r= |
| By: | van Beek, Andries (Tilburg University, Center For Economic Research); Malmberg, Benjamin; Borm, Peter (Tilburg University, Center For Economic Research); Quant, Marieke (Tilburg University, Center For Economic Research); Schouten, Jop (Tilburg University, Center For Economic Research) |
| Keywords: | biform games; pure Nash equilibria; linear production; Owen set; sequencing; gain splitting rule |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:fd7a301b-7ef3-4142-835d-a49243578893&r= |
| By: | JOHN HILLAS; DMITRIY KVASOV |
| Abstract: | We show that two strategies are Kuhn equivalent if and only if they induce the same probability measure over ter- minal nodes against some profile of completely mixed behaviour strategies of the other players. This result allows us to embed the equivalence classes of strategies in the probability measures over terminal nodes for various strategy concepts. This, in turn, allows a very clean statement of the relation between the various sets of strategies in games with perfect recall, linear games, and nonlin- ear games. It also proves useful in defining and analysing solution concepts in games without perfect recall, and, in particular, in nonlinear games. |
| Keywords: | extensive form games; perfect recall; linear games; non- linear games; Kuhn equivalence. |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2021&r= |
| By: | Gáfaro, Margarita; Mantilla, Cesar |
| Abstract: | We characterize a general bargaining game useful for environmental valuation purposes. In this game, a jointly endowed asset is divisible into smaller units of two types: those with and without an associated costly attribute. Bargaining parties can use monetary transfers to their counterpart in exchange for accruing more units of the jointly endowed asset. We show that the cost of the attribute is perfectly absorbed by the transfer in a broad set of game solutions. Outcomes differing in the allocation of the units with the costly attribute allows us to identify whether the players' valuation of the attribute corresponds to its value induced in the game (i.e., its cost) or whether this attribute is over-or under-valued. We show an application to the valuation of water in a lab-in-the-field experiment conducted with Colombian farmers. We find evidence that the players' valuation of in-plot access to water dwells between 2.1 and 3.5 times its induced cost in the experiment. |
| Date: | 2021–04–19 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:tcfyb&r= |
| By: | Celen, Ihsan; Saglam, Ismail |
| Abstract: | We consider an infinitely-lived duopoly with asymmetric costs and study the incentives of the firms to collude or compete in supply functions under the possibility of technology licensing. Simulating the subgame-perfect Nash equilibria of alternative industry organizations, we show that licensing makes collusion harder; but it always has a positive effect on the welfares of consumers and the less efficient firm in the duopoly. |
| Keywords: | Duopoly; collusion; supply function equilibrium; licensing. |
| JEL: | D43 L13 O30 |
| Date: | 2021–04–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107261&r= |
| By: | Galit Ashkenazi-Golan; Yevgeny Tsodikovich; Yannick Viossat |
| Abstract: | A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a Best and Final Offer (BAFO) stage. This final bid can depend on new information provided about either the asset or the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information settings. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer to not reveal information. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.09942&r= |
| By: | Damiano Brigo; Xiaoshan Huang; Andrea Pallavicini; Haitz Saez de Ocariz Borde |
| Abstract: | Deep learning is a powerful tool whose applications in quantitative finance are growing every day. Yet, artificial neural networks behave as black boxes and this hinders validation and accountability processes. Being able to interpret the inner functioning and the input-output relationship of these networks has become key for the acceptance of such tools. In this paper we focus on the calibration process of a stochastic volatility model, a subject recently tackled by deep learning algorithms. We analyze the Heston model in particular, as this model's properties are well known, resulting in an ideal benchmark case. We investigate the capability of local strategies and global strategies coming from cooperative game theory to explain the trained neural networks, and we find that global strategies such as Shapley values can be effectively used in practice. Our analysis also highlights that Shapley values may help choose the network architecture, as we find that fully-connected neural networks perform better than convolutional neural networks in predicting and interpreting the Heston model prices to parameters relationship. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.09476&r= |
| By: | Damien, Besancenot (Université de Paris Descartes); Radu, Vranceanu (ESSEC Research Center, ESSEC Business School) |
| Abstract: | This paper reports the results from a two-person "pledge and give" experiment. Each persons endowment is private information available only to him. In the first stage, each agent informs the other about the amount he intends to give, or makes a pledge. In the second stage, each agent makes a contribution to the joint donation. A simple theoretical model shows that in this game the equilibrium pledge function is linear in the endowment of each agent. Furthermore, if agents have a strong taste for conformity, the optimal gift is positively related to one's own endowment and to the pledge of his partner. Data from the lab experiment show that, indeed, subjects pledge approximately 60% of their endowment. Also, pledges have an important social influence role: an agent will increase his donation by 20 cents on average if his partner pledges one more euro. |
| Keywords: | Charity giving; Conformity; Strategic pledges; Social influence |
| JEL: | C92 D64 D83 |
| Date: | 2019–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-19007&r= |
| By: | Hopp, Daniel |
| Abstract: | The external validity of dictator games conducted in a lab is often questioned due to the use of small stake sizes that do not correspond to real-world settings. A potential solution to this problem is based on how participant perceptions of stake sizes are affected by their numerical representation. In this paper, I vary the stake size and its numerical representation to examine whether the illusion of large stakes can be created convincingly by implementing inflated numbers through an experimental currency. The share allocated to the recipient does not differ across treatments in this large-sample online experiment. This finding demonstrates that neither an increase in stake size nor a change in its numerical representation influence the share allocated to the recipient in a dictator game. |
| Keywords: | dictator game,stake size,numerosity |
| JEL: | C99 D64 D91 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cawmdp:123&r= |
| By: | Nobuyuki Hanaki; Aidas Masiliunas |
| Abstract: | Multiple Cournot oligopoly experiments found more collusive behavior in markets with fewer firms (Huck et al., 2004; Hostmann et al., 2018). This result could be explained by a higher difficulty to coordinate or by lower incentives to collude in markets with more firms. We show that the Quantal Response Equilibrium can explain how the change in incentives alone could result in more collusive output in smaller markets. We propose a new method to manipulate the group size while keeping constant the locations of key outcomes, payoffs at these outcomes and the incentives to collude. Experiments using this normalized payoff function find that the number of firms has no direct effect on the average output or profit. We conclude that higher rates of aggregate collusion in markets with fewer firms are driven by the changes in incentives or focality rather than purely the number of firms. These findings imply that antitrust policies aimed at preventing collusion should focus on incentives rather than on the market concentration. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1131&r= |
| By: | Nika Haghtalab; Nicole Immorlica; Brendan Lucier; Markus Mobius; Divyarthi Mohan |
| Abstract: | We study a model of social learning and communication using hard anecdotal evidence. There are two Bayesian agents (a sender and a receiver) who wish to communicate. The receiver must take an action whose payoff depends on their personal preferences and an unknown state of the world. The sender has access to a collection of n samples correlated with the state of the world, which we think of as specific anecdotes or pieces of evidence, and can send exactly one of these samples to the receiver in order to influence her choice of action. Importantly, the sender's personal preferences may differ from the receiver's, which affects the seller's strategic choice of which anecdote to send. We show that if the sender's communication scheme is observable to the receiver (that is, the choice of which anecdote to send given the set they receive), then they will choose an unbiased and maximally informative communication scheme, no matter the difference in preferences. Without observability, however, even a small difference in preferences can lead to a significant bias in the choice of anecdote, which the receiver must then account for. This can significantly reduce the informativeness of the signal, leading to substantial utility loss for both sides. One implication is informational homophily: a receiver can rationally prefer to obtain information from a poorly-informed sender with aligned preferences, rather than a knowledgeable expert whose preferences may differ from her own. |
| JEL: | G4 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:28661&r=all |
| By: | Lin Hu; Anqi Li; Xu Tan |
| Abstract: | A group of heterogeneous players gathers information about an uncertain state before making decisions. Each player allocates his limited bandwidth between biased sources and the other players, and the resulting stochastic attention network facilitates the transmission of news from sources to him either directly or indirectly through the other players. The limit in the bandwidth leads the player to focus on his own-biased source, resulting in occasional cross-cutting exposures but most of the time a reinforcement of his predisposition. It also confines his attention to like-minded friends who, by attending to the same primary source as his, serve as secondary sources in case the news transmission from the primary source to him is disrupted. A mandate on impartial exposures to all biased sources disrupts echo chambers but entails ambiguous welfare consequences. Inside an echo chamber, even a small amount of heterogeneity between players can generate fat-tailed distributions of public opinion, and factors affecting the visibility of sources and players could have unintended consequences for public opinion and consumer welfare. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.10657&r= |
| By: | Chenwei Shi; Yiyang Wang |
| Abstract: | This paper approaches the problem of understanding collective agency from a logical and game-theoretical perspective. Instead of collective intentionality, our analysis highlights the role of Pareto optimality. To facilitate the analysis, we propose a logic of preference and functional dependence by extending the logic of functional dependence. In this logic, we can express Pareto optimality and thus reason about collective agency. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.09112&r= |
| By: | Arno Riedl; Ingrid M. T. Rohde; Martin Strobel |
| Abstract: | Situations where independent agents need to align their activities to achieve individually and socially beneficial outcomes are abundant, reaching from everyday situations like fixing a time for a meeting to global problems like climate change agreements. Often such situations can be described as stag-hunt games, where coordinating on the socially efficient outcome is individually optimal but also entails a risk of losing out. Previous work has shown that in fixed interaction neighborhoods agents’ behavior mostly converges to collectively inefficient outcome. However, in the field, interaction neighborhoods often can be self-determined. Theoretical work investigating such circumstances is ambiguous in whether the efficient or inefficient outcome will prevail. We performed an experiment with human subjects exploring how free neighborhood choice affects coordination. In a fixed interaction treatment, a vast majority of subjects quickly coordinates on the inefficient outcome. In a treatment with neighborhood choice, the outcome is dramatically different: behavior quickly converges to the socially desirable outcome leading to welfare gains 2.5 times higher than in the environment without neighborhood choice. Participants playing efficiently exclude those playing inefficiently who in response change their behavior and are subsequently included again. Importantly, this mechanism is effective despite that only few exclusions actually occur. |
| Keywords: | stag-hunt, neighborhood choice, coordination, social welfare, exclusion |
| JEL: | C72 C90 D03 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9012&r= |
| By: | Sutan, Angela (University Bourgogne Franche-Comte, Burgundy School of Business-); Vranceanu, Radu (ESSEC Research Center, ESSEC Business School) |
| Abstract: | This paper reports the results from a lab experiment in which subjects playing the manager role can implement either an efficient / inegalitarian allocation or an inefficient / egalitarian allocation of payoffs. The experiment simulates a stylized managerial context by allowing the manager to manipulate information and select the decision process and by allowing the stakeholders to retaliate against the manager given different choices in the decision process. We found that the inefficient allocation is often selected and that this choice depends on whether the employees can retaliate against the manager and on whether the manager can hide information about the payoffs. The social preferences of the manager also explain the choice of the option. However, the decision process and the managerial style based on self-reported attitudes have little influence on the choice of allocation. This is consistent with employee satisfaction essentially depending on the payoff and not being sensible to the process. |
| Keywords: | Management style; Managerial decision; Decision process; Asymmetric information; Communication strategy |
| JEL: | C92 D39 M12 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-19010&r= |
| By: | Vladimir A. Karamychev; Jean-Marie Viaene |
| Abstract: | Mobile payments (m-payments) increase the accessibility of large segments of society to financial services while before the traditional banking system excluded these for lack of proof of identity and because of unsafe environments. This constitutes a key driver of new growth strategies of the developing world. Smartphones are essential to perform m-payments. In that regard, recent criticism from different sides has expressed the view that manufacturers’ strategies generate partial market coverage whereby the purchase of a phone and financial inclusion also remain out of reach for the group of poor consumers. Our aim in this paper is to examine the theoretical premises of this conjecture in a small open economy and uncover the conditions under which full market coverage is efficient and desirable. We analyze subgame perfect equilibria of a vertical duopoly model characterized by consumers’ taste for quality. The government uses taxes and/or subsidies to modify the market equilibrium. Given this, the following issues are considered: (a) What is the impact of different standards of payment security on the equilibrium number of low- and high-quality users? (b) What are the aggregate welfare gains of complete financial inclusion? (c) What happens if phone makers are foreign? |
| Keywords: | vertical duopoly, full market coverage, technical obsolescence, financial inclusion |
| JEL: | F23 G50 H31 H62 L13 L15 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8995&r= |