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on Game Theory |
| By: | Olaizola, Norma; Valenciano, Federico |
| Abstract: | We study a connections model where the strength of a link depends on the amount invested in it and is determined by an increasing strictly concave function. The revenue from investments in links is the information that the nodes receive through the network. First, the structures of efficient networks are characterized, and conditions for optimal investments constrained to supporting a given network are obtained. Second, assuming that links are the result of investments by the node-players involved, there is the question of stability. We introduce and characterize a notion of marginal equilibrium weaker than that of Nash equilibrium, and identify different marginally stable structures. Efficiency and stability are shown to be incompatible, but partial subsidizing is shown to be able to bridge the gap. |
| Keywords: | Networks, Connections model, Decreasing returns, Efficiency, Stability. |
| JEL: | A14 C72 D85 |
| Date: | 2020–10–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107585&r= |
| By: | Yevgeny Tsodikovich (Aix Marseille Univ, CNRS, AMSE, Marseille, France.); Xavier Venel (Dipartimento di Economia e Finanza, LUISS, Rome, Italy.); Anna Zseleva (Maastricht University, School of Business and Economics, Dept. of Quantitative Economics, Maastricht, The Netherlands) |
| Abstract: | We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation. |
| Keywords: | switching costs, repeated games, stochastic games, zero-sum games |
| JEL: | C72 C73 |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:2129&r= |
| By: | Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are ``self-destroying'' as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable strategies. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process. |
| Keywords: | Self-confirming equilibrium, conjectural equilibrium, extensive-form rationalizability, unawareness, extensive-form games, equilibrium, learning, discovery |
| JEL: | C72 D83 |
| Date: | 2021–05–05 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:340&r= |
| By: | Besner, Manfred |
| Abstract: | We introduce a new value for games with transferable utility, called grand dividends value. In the payoff calculation, the grand dividends value takes into account the worths of all subcoalitions of a player set. The concept of grand dividends, representing the surplus (which can also be non-positive) of the worth of the grand coalition over the worths of all coalitions that lack one player of the player set, is the initial point here. The grand dividends value satisfies many properties that we know from the Shapley value. Along with new axioms that have a similar correspondence to axioms that are also satisfied by the Shapley value, axiomatizations arise that have an analogous equivalent for the Shapley value, including the classics of Shapley and Young. |
| Keywords: | Cooperative game; (Harsanyi/Grand) Dividends; Shapley value; Grand dividends value |
| JEL: | C7 C71 |
| Date: | 2021–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107615&r= |
| By: | Koessler, Frederic; Skreta, Vasiliki |
| Abstract: | A designer is privately informed about the state and chooses an information disclosure mechanism to influence the decisions of multiple agents playing a game. We define an intuitive class of incentive compatible information disclosure mechanisms which we coin interim optimal mechanisms. We prove that an interim optimal mechanism exists, and that it is an equilibrium outcome of the interim information design game. An ex-ante optimal mechanism may not be interim optimal, but it is whenever it is ex-post optimal. In addition, in leading settings in which action sets are binary, every ex-ante optimal mechanism is interim optimal. We relate interim optimal mechanisms to other solutions of informed principal problems. |
| Keywords: | Bayesian persuasion; core mechanism; Informed principal; interim information design; neutral optimum; strong-neologism proofness; verifiable types |
| JEL: | C72 D82 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15709&r= |
| By: | Arega Getaneh Abate; Rosana Riccardi; Carlos Ruiz |
| Abstract: | Demand response (DR) programs have gained much attention during the last three decades to optimize the decisions of the electricity market participants considering the demand-side management (DSM). It can potentially enhance system reliability and manages price volatility by modifying the amount or time of electricity consumption. This paper proposes a novel game-theoretical model accounting for the relationship between retailers (leaders) and consumers (followers) in a dynamic price environment where both players optimize their respective economic goals under uncertainty. The model is solved under two frameworks. First by considering retailer's market power and second by accounting for an equilibrium setting based on a Cournot game. These are formulated in terms of a mathematical program with equilibrium constraints (MPEC) and with a mixed-integer linear program (MILP), respectively. In particular, the retailers' market power model is first formulated as a bi-level optimization problem, and the MPEC is subsequently derived by replacing the consumers' problem (lower level) with its Karush-Kuhn-Tucker (KKT) optimality conditions. In contrast, the Cournot equilibrium model is solved as a MILP by concatenating the retailer's and consumers' KKT optimality conditions. The solution sets, the practical approaches for solutions, the required techniques to test and compare the performance of the model are undertaken with realistic data. Numerical simulations confirm the applicability and effectiveness of the proposed model to explore the interactions of markets power and DR programs. The results confirm that consumers are better off in an equilibrium framework while the retailer increases its expected profit when the market power is considered. However, we show how these results are highly affected by the levels of of consumers' flexibility. |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2105.03405&r= |
| By: | Nocke, Volker; Strausz, Roland |
| Abstract: | We develop a theory of collective brand reputation for markets in which product quality is jointly determined by local and global players. In a repeated game of imperfect public monitoring, we model collective branding as a pooling of quality signals generated in different markets. Such pooling yields a beneficial informativeness effect for the actions of a global player present in all markets, but also harmful free-riding by local, market-specific players. The resulting tradeoff yields a theory of optimal brand size and revenue sharing, applying to platform markets, franchising, licensing, umbrella branding, and firms with team production. |
| Keywords: | Collective branding; free riding; Imperfect Monitoring; repeated games; reputation |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15732&r= |
| By: | Sam Ganzfried |
| Abstract: | Many real-world games contain parameters which can affect payoffs, action spaces, and information states. For fixed values of the parameters, the game can be solved using standard algorithms. However, in many settings agents must act without knowing the values of the parameters that will be encountered in advance. Often the decisions must be made by a human under time and resource constraints, and it is unrealistic to assume that a human can solve the game in real time. We present a new framework that enables human decision makers to make fast decisions without the aid of real-time solvers. We demonstrate applicability to a variety of situations including settings with multiple players and imperfect information. |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2104.14744&r= |
| By: | Cabrales, Antonio; Feri, Francesco; Gottardi, Piero; Meléndez-Jiménez, Miguel A. |
| Abstract: | This paper reports on experiments regarding cheap talk games where senders attempt deception when their interests are not in conflict with those of the receiver. The amount of miscommunication is higher than in previous experimental findings on cheap talk games in situations where senders' and receivers' interests are not in conflict. We obtain this even though, as in previous literature, some participants appear to feature a cost of lying. We argue our findings could be attributed to distributional preferences of senders who lie to avoid the receiver getting a higher payoff than herself. |
| Keywords: | cheap talk; Conflicts of interest; Deception; Experiments; social preferences |
| JEL: | C72 D83 G14 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15711&r= |
| By: | Bochet, Olivier; Faure, Mathieu; Long, Yan; Zenou, Yves |
| Abstract: | Agents compete for the same resources and are only aware of their direct neighbors in a network. We propose a new equilibrium concept, referred to as peer-consistent equilibrium (PCE). In a PCE, each agent chooses an effort level that maximizes her subjective perceived utility and the effort levels of all individuals in the network need to be consistent. We develop an algorithm that breaks the network into communities. We use this decomposition to completely characterize peer-consistent equilibria by identifying which sets of agents can be active in equilibrium. An agent is active if she either belongs to a strong community or if few agents are aware of her existence. We show that there is a unique stable PCE. We provide a microfoundation of eigenvector centrality, since, in any stable PCE, agents' effort levels are proportional to their eigenvector centrality in the network. |
| Keywords: | eigenvector centrality; policies; Social Networks |
| JEL: | C72 D85 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15582&r= |
| By: | Saccal, Alessandro |
| Abstract: | The following contributions are hereby worked: one mathematically formalises Mundell’s Impossible trio and Rodrik’s Globalisation paradox, supplying the latter with a taxonomy in terms of the current account; by means of Kaldor’s price endogeneity in output, one proves that external real money market disparity and trade generate external output mismatches and lead to autarky unless offset, using topology and dynamical systems; one characterises transfers and federalism and shows that all unitary states are federal polities and can merge into confederations; one demonstrates that the said external output mismatches can be only eluded via autarky or neutralisation, irrespective of federalism; one discerns artificial currency areas guaranteeing inter-regional external output equality and modern protectionism as two Nash equilibria, especially rationalising the nexus between the Gold standard, the Industrial revolution and the Great divergence therethrough. |
| Keywords: | autarky; federalism; inefficiency; trilemma. |
| JEL: | E12 F13 F22 F41 F43 F45 F52 F60 N10 O11 O40 |
| Date: | 2019–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:107639&r= |
| By: | Gaonkar, Shweta; Mele, Angelo (Johns Hopkins University) |
| Abstract: | How do inter-organizational networks emerge? Accounting for interdependence among ties while studying tie formation is one of the key challenges in this area of research. We address this challenge using an equilibrium framework where firms' decisions to form links with other firms are modeled as a strategic game. In this game, firms weigh the costs and benefits of establishing a relationship with other firms and form ties if their net payoffs are positive. We characterize the equilibrium networks as exponential random graphs (ERGM), and we estimate the firms' payoffs using a Bayesian approach. To demonstrate the usefulness of our approach, we apply the framework to a co-investment network of venture capital firms in the medical device industry. The equilibrium framework allows researchers to draw economic interpretation from parameter estimates of the ERGM Model. We learn that firms rely on their joint partners (transitivity) and prefer to form ties with firms similar to themselves (homophily). These results hold after controlling for the interdependence among ties. Another, critical advantage of a structural approach is that it allows us to simulate the effects of economic shocks or policy counterfactuals. We test two such policy shocks, namely, firm entry and regulatory change. We show how new firms' entry or a regulatory shock of minimum capital requirements increase the co-investment network's density and clustering. |
| Date: | 2021–05–05 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:ysbmq&r= |
| By: | Konrad, Kai A.; Morath, Florian |
| Abstract: | We study the long-run stochastic stability properties of volunteering strategies in finite populations. We allow for mixed strategies, characterized by the probability that a player may not volunteer. A pairwise comparison of evolutionary strategies shows that the strategy with a lower probability of volunteering is advantaged. However, in the long run there are also groups of volunteering types. Homomorphisms with the more volunteering types are more frequent if the groups have fewer members, and if the benefits from volunteering are larger. Such homomorphisms with volunteering cease to exist if the group becomes infinitely large. In contrast, the disadvantage of volunteering disappears if the ratio of individual benefits and costs of volunteering becomes infinitely large. |
| Keywords: | collective action; finite populations; Mixed strategies; stochastic stability; volunteering |
| JEL: | C73 D62 H41 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15536&r= |
| By: | Pycia, Marek; Woodward, Kyle |
| Abstract: | The pay-as-bid (or discriminatory) auction is a prominent format for selling homogenous goods such as treasury securities and commodities. We prove the uniqueness of its pure-strategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids. Building on these results we analyze the optimal design of pay-as-bid auctions, as well as uniform-price auctions (the main alternative auction format), allowing for asymmetric information. We show that supply transparency and full disclosure are optimal in pay-as-bid, though not necessarily in uniform-price; pay-as-bid is revenue dominant and might be welfare dominant; and, under assumptions commonly imposed in empirical work, the two formats are revenue and welfare equivalent. |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15656&r= |
| By: | Casella, Alessandra; Friedman, Evan; Perez Archila, Manuel |
| 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. |
| Keywords: | Conflict resolution; Laboratory experiments; mechanism design; mediation |
| JEL: | C78 C92 D74 D82 D86 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15483&r= |
| By: | Calvi, Rossella; Keskar, Ajinkya |
| Abstract: | We develop a non-cooperative bargaining model with incomplete information linking dowry payments, domestic violence, resource allocation between a husband and a wife, and separation. Our model generates several predictions, which we test empirically using amendments to the Indian anti-dowry law as a natural experiment. We document a decline in women's decision-making power and separations, and a surge in domestic violence following the amendments. These unintended effects are attenuated when social stigma against separation is low and, in some circumstances, when gains from marriage are high. Whenever possible, parents increase investment in their daughters' human capital to compensate for lower dowries. |
| Keywords: | Domestic violence; dowry; India; marital surplus; Non-cooperative bargaining; Women's Empowerment |
| JEL: | D13 I31 J12 O15 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15696&r= |
| By: | Perez-Richet, Eduardo; Skreta, Vasiliki |
| Abstract: | We study the optimal design of tests with manipulable inputs: data, actions, reports. An agent can, at a cost, falsify the input into the test, or state of the world, so as to influence the downstream binary decision of a receiver informed by the test. We characterize receiver-optimal tests under different constraints. Under covert falsification, the receiver-optimal test is inefficient. With a rich state space, it involves equilibrium falsification at a possibly large cost to the agent, and may therefore exert a negative social externality. The receiver-optimal test that is immune to falsification, while also inefficient, strictly improves the payoff of the agent. When the falsification strategy of the agent is observable, or can be committed to, the receiver-optimal test is efficient, uses a rich signal space, and gives the receiver at least half of his full information payoff. |
| Keywords: | Bayesian persuasion; Cheating; Falsification; information design; manipulation; Tests |
| JEL: | C72 D82 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15627&r= |
| By: | Wanchang Zhang |
| Abstract: | We study the design of auction within the correlation-robust framework in which the auctioneer is assumed to have information only about marginal distributions, but does not know the correlation structure of the joint distribution. The performance of a mechanism is evaluated in the worst-case over the uncertainty of joint distributions that are consistent with the marginal distributions. For the two-bidder case, we characterize the Second Price Auction with Uniformly Distributed Reserves as a maxmin auction among dominant strategy incentive compatible (DSIC) and ex-post individually rational (EPIR) mechanisms under the robust-version regularity conditions. For the $N$-bidder ($N\ge 3$) case, we characterize the Second Price Auction with $Beta (\frac{1}{N-1},1)$ Distributed Reserves as a maxmin auction among exclusive (a bidder whose bid is not the highest will never be allocated) DSIC and EPIR mechanisms under the general robust-version regularity conditions (I). |
| Date: | 2021–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2105.04697&r= |
| By: | Eliaz, Kfir; Frug, Alexander |
| Abstract: | We introduce a new reason for why an informed sender may not be able to communicate(via cheap talk) his private information to an uninformed receiver. Our framework has two novel features: (i) conditional on interacting, both parties agree on the optimal action to take given the sender's information, and (ii) there are some sender types (the "toxic" types) with which the receiver prefers not to interact. Our main result establishes that for a broad class of preferences, any interval equilibrium (where each message is associated with an interval of types) induces only finitely many actions in the support of the receiver's strategy. For a canonical class of preferences with uniformly distributed types, we characterize the Pareto efficient(interval) equilibria and illustrate how communication is adversely affected even with a small set of toxic types. In addition, we show that introducing a second stage in which the receiver gets a noisy signal on the sender type can have a dramatic effect on the first-stage communication. |
| Keywords: | cheap talk; contagion |
| JEL: | D83 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15511&r= |
| By: | Goldlücke, Susanne; Tröger, Thomas |
| Abstract: | We consider mechanisms for assigning an unpleasant task among a group of agents with heterogenous abilities. We emphasize threshold rules: every agent decides whether or not to ``volunteer''; if the number of volunteers exceeds a threshold number, the task is assigned to a random volunteer; if the number is below the threshold, the task is assigned to a random non-volunteer. We show that any non-extreme threshold rule allows for a symmetric equilibrium in which every ability type is strictly better off than in a random assignment. This holds for arbitrarily high costs of performing the task. Within the class of binary-action mechanisms, some threshold rule is utilitarian optimal. The first-best can be approximated arbitrarily closely with a threshold rule as the group size tends to infinity; that is, there exist threshold numbers such that with probability arbitrarily close to 1 the task is performed by an agent with an ability arbitrarily close to the highest possible ability. The optimal threshold number goes to infinity as the group size tends to infinity. |
| Keywords: | mechanism design without transfers; Public Good Provision; volunteering |
| JEL: | D82 H41 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15580&r= |
| By: | Xiaoyang He; Ralph Siebert |
| Abstract: | We consider a dynamic oligopoly on the beer market and study the differential effects of switching costs on product prices, market shares, and profits. Our demand estimation results show large differences in brand loyalty, and switching costs across customer income segments and beer brands. Our supply estimation results show that the low-quality firm experiences a higher competitive pressure on price since low-quality consumers are more price sensitive and switch more easily to the high-quality firm’s product than vice versa. The high-quality firm is better shielded from price competition, as its consumers are less likely to switch to the low-quality product. |
| Keywords: | consumer heterogeneity, differentiated products, dynamic oligopoly, dynamic pricing, loyalty, state dependence, switching costs |
| JEL: | L13 L25 L66 M21 M31 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9065&r= |
| By: | Hernán Bejarano (Centro de Investigación y Docencia en Economía de México/Chapman University); Joris Gillet (Middlesex University); Ismael Rodríguez-Lara (Chapman University/Universidad de Granada) |
| Abstract: | We investigate experimentally the effect of a negative endowment shock in a trust game to assess whether different causes of inequality have different effects on trust and trustworthiness. In our trust game there may be inequality in favor of the second mover and this may (or may not) be the result of a negative random shock (i.e., the outcome of a die roll) that decreases the endowment of the first-mover. Our findings suggest that inequality leads to differences in behavior. First-movers send more of their endowment and second-movers return more when there is inequality. However, we do not find support for the hypothesisthat the cause of the inequality matters. Behavior after the occurrence of a random shock is not significantly different from the behavior when the inequality exists from the outset. Our results highlight that we have to be cautious when interpreting the effects on trust and trustworthiness of negative random shocks that occur in the field (e.g., natural disasters). Our results suggest that these effects are largely driven by the inequality caused by the shock and not by any of the additional characteristics of the shock like saliency or uncertainty. |
| Keywords: | Trust game endowment heterogeneity random shocks inequality aversion experimental economics |
| JEL: | C91 D02 D03 D69 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:50&r= |
| By: | Canen, Nathan; Kendall, Chad; Trebbi, Francesco |
| Abstract: | The current polarization of elites in the U.S., particularly in Congress, is frequently ascribed to the emergence of cohorts of ideologically extreme legislators replacing moderate ones. Politicians, however, do not operate as isolated agents, driven solely by their preferences. They act within organized parties, whose leaders exert control over the rank-and-file, directing support for and against policies. This paper shows that the omission of party discipline as a driver of political polarization is consequential for our understanding of this phenomenon. We present a multi-dimensional voting model and identification strategy designed to decouple the ideological preferences of lawmakers from the control exerted by their party leadership. Applying this structural framework to the U.S. Congress between 1927- 2018, we find that the influence of leaders over their rank-and-file has been a growing driver of polarization in voting, particularly since the 1970s. In 2018, party discipline accounts for around 65% of the polarization in roll call voting. Our findings qualify the interpretation of â?? and in two important cases subvert â?? a number of empirical claims in the literature that measures polarization with models that lack a formal role for parties. |
| Keywords: | discipline; Ideology; Parties; Political Polarization; Spatial voting |
| JEL: | D72 P48 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:15607&r= |