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on Game Theory |
| By: | Hannu Salonen (University of Turku); Mitri Kitti (University of Turku) |
| Abstract: | We give a proof of the existence of a Nash equilibrium forn-personnormal form games when each player’s utility function is continuousw.r.t. strategy profiles, and concave and differentiable w.r.t. his ownstrategy. The proof uses only elementary mathematical tools such asmathematical induction. We show that this equilibrium existence re-sult is sufficiently general to imply the Brouwer Fixed Point Theorem.The Kakutani Fixed Point Theorem is obtained as a corollary by usingstandard techniques. |
| Keywords: | Nash equilibrium, fixed-point theorem |
| JEL: | C72 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp131&r=all |
| By: | Calleja, Pedro (Departament de Matemàtica Econòmica); Llerena, Francesc (Departament de Gestió dEmpreses); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We introduce the constrained egalitarian surplus-sharing rule fCE, which distributes an amount of a divisible resource so that the poorer agents’ resulting payoffs become equal but not larger than any remaining agent’s status quo payoff. We show that fCE is characterized by Pareto optimality, nonnegativity, path independence, and less first, a new property requiring that an agent does not gain if her status quo payoff exceeds that of another agent by the surplus. We provide two additional characterizations weakening less first and employing consistency, a classical invariance property with respect to changes of population. We investigate the effects of egalitarian principles in the setting of transferable utility (TU) games. A single-valued solution for TU games is said to support constrained welfare egalitarianism if it distributes any increment of the worth of the grand coalition according to fCE. We show that the set of Pareto optimal single-valued solutions that support fCE is characterized by means of aggregate monotonicity and bounded pairwise fairness, resembling less first. |
| Keywords: | Surplus-sharing problem; egalitarianism; Lorenz domination; TU game |
| JEL: | C71 |
| Date: | 2020–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2020_001&r=all |
| By: | Bergantiños, Gustavo; Navarro-Ramos, Adriana |
| Abstract: | This paper considers agglomeration economies. A new firm is planning to open a plant in a country divided into several regions. Each firm receives a positive externality if the new plant is located in its region. In a decentralized mechanism, the plant would be opened in the region where the new firm maximizes its individual benefit. Due to the externalities, it could be the case that the aggregated utility of all firms is maximized in a different region. Thus, the firms in the optimal region could transfer something to the new firm in order to incentivize it to open the plant in that region. We propose two rules that provide two different schemes for transfers between firms already located in the country and the newcomer. The first is based on cooperative game theory. This rule coincides with the nucleolus and the t-value of the associated cooperative game. The second is defined directly. We provide axiomatic characterizations for both rules. We characterize the core of the cooperative game. We prove that both rules belong to the core. |
| Keywords: | game theory, core, axiomatic characterization, agglomeration economies. |
| JEL: | C71 |
| Date: | 2020–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98121&r=all |
| By: | Duk Gyoo Kim; Wooyoung Lim |
| Abstract: | Many-player divide-the-dollar games have been a workhorse in the theoretical and experimental analysis of multilateral bargaining. If we are dealing with a loss, that is, if we consider many-player “divide-the-penalty” games for, e.g., the location choice of obnoxious facilities, the allocation of burdensome chores, or the reduction of carbon dioxide emissions at a climate change summit, the theoretical predictions do not merely flip the sign of those in the divide-the-dollar games. We show that the stationary subgame perfect equilibrium (SSPE) is no longer unique in payoffs. The most “egalitarian” equilibrium among the stationary equilibria is a mirror image of the essentially unique SSPE in the Baron-Ferejohn model. That equilibrium is fragile in the sense that allocations are sensitive when responding to changes in parameters, while the most “unequal” equilibrium is not affected by changes in parameters. Experimental evidence clearly supports the most unequal equilibrium: Most of the approved proposals under a majority rule involve an extreme allocation of the loss to a few members. Other observations such as no delay, proposer advantage, and the acceptance rate are also consistent with the predictions based on the most unequal equilibrium. |
| Keywords: | multilateral bargaining, loss division, laboratory experiments |
| JEL: | C78 D72 C92 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8011&r=all |
| By: | Hakobyan, Zaruhi; Koulovatianos, Christos |
| Abstract: | Differential games of common resources that are governed by linear accumulation constraints have several applications. Examples include political rent-seeking groups expropriating public infrastructure, oligopolies expropriating common resources, industries using specific common infrastructure or equipment, capital-flight problems, pollution, etc. Most of the theoretical literature employs specific parametric examples of utility functions. For symmetric differential games with linear constraints and a general time-separable utility function depending only on the player's control variable, we provide an exact formula for interior symmetric Markovian-strategies. This exact solution, (a) serves as a guide for obtaining some new closed-form solutions and for characterizing multiple equilibria, and (b) implies that, if the utility function is an analytic function, then the Markovian strategies are analytic functions, too. This analyticity property facilitates the numerical computation of interior solutions of such games using polynomial projection methods and gives potential to computing modified game versions with corner solutions by employing a homotopy approach. |
| Keywords: | differential games,endogenous growth,tragedy of the commons,Lagrange-d'Alembert equation,analytic functions |
| JEL: | C73 C61 D74 E0 O40 O44 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:638&r=all |
| By: | Matteo Triossi; María Haydée Fonseca-Mairena |
| Abstract: | We study the implementability of stable correspondences in marriage markets with externalities. We prove that, contrary to what happens in markets without externalities, no stable revelation mechanism makes a dominant strategy for the agents on one side of the market to reveal their preferences. However, the stable correspondence in implementable in Nash equilibrium. JEL Codes:Economic Literature Classification Numbers: C72, C78, D62, D78. Key words: Marriage market with externalities; Incentives; Implementation. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:344&r=all |
| By: | Crawford, Vincent P |
| Keywords: | Behavioral game theory, Experimental game theory, Strategic thinking, Level-k models, Coordination, Salience, Applied Economics, Economics |
| Date: | 2018–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt99q8h4pt&r=all |
| By: | Dan Kovenock (Economic Science Institute, Chapman University); Jingfeng Lu (Department of Economics, National University of Singapore) |
| Abstract: | In this paper, we study score procurement auctions with all-pay quality bids. A supplierís score is the di§erence between his quality and price bids. The supplier with the highest score wins and gets paid his own price bid. The procurerís payo§ is the di§erence between the winnerís quality and the procurerís payments to the suppliers. Equilibrium quality and price bids are solved without Örst obtaining the corresponding equilibrium scores. We Önd that quality bids, the suppliersípayo§s and the procurerís payo§ do not depend on whether price bids are made contingent on quality bids. Compared to a benchmark of winner-pay quality bids, in which the losing suppliersí quality bidding costs are reimbursed by the procurer, all-pay quality bids tend to reduce quality provision and suppliersípayo§s, but they tend to increase the total surplus and the procurerís payo§. |
| Keywords: | All-pay quality bids, Equilibrium analysis, Score auctions, Score procurements, Winner-pay quality bid |
| JEL: | C70 D44 D89 L12 O32 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-01&r=all |
| By: | Federica Alberti (Portsmouth Business School); Anna Conte (Sapienza University of Rome); Daniela T. Di Cagno (LUISS Guido Carli University); Emanuela Sciubba (Birkbeck University of London) |
| Abstract: | Our social lives are governed by trust. But how do we choose whom to trust? In this work, based on a laboratory experiment, we explore whether building relationships in a social network increases individuals' level of trust. We find that social interactions direct trust, but their impulse is not sufficiently strong to result beneficial. |
| Keywords: | Social network, Trust, Lab experiment |
| JEL: | C72 C91 C92 D82 D85 |
| Date: | 2020–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:pbs:ecofin:2020-02&r=all |
| By: | Howell, William; Shepsle, Kenneth; Wolton, Stephane |
| Abstract: | Separated powers cannot permanently constrain individual ambitions. Concerns about a government's ability to respond to contemporary and future crises, we show, invariably compromise the principled commitments one branch of government has in limiting the authority of another. We study a dynamic model in which a politician (most commonly an executive) makes authority claims that are subject to a hard constraint (administered, typically, by a court). At any period, the court is free to rule against the executive and thereby permanently halt her efforts to acquire more power. Because it appropriately cares about the executive's ability to address real-world disruptions, however, the court is always willing to affirm more authority. Neither robust electoral competition nor alternative characterizations of judicial rule fundamentally alters this state of affairs. The result, we show, is a persistent accumulation of executive authority. |
| Keywords: | Authority, Executive Growh, Judicial Decision, Separation of Power, Federalist |
| JEL: | C73 D02 D70 D72 H11 K39 |
| Date: | 2020–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98221&r=all |
| By: | Castillo, Geoffrey; Choo, Lawrence; Grimm, Veronika |
| Abstract: | Groups are often found to be more rational than individuals. In lying games, this implies that groups are more dishonest. We scrutinise this conclusion in a setup where there are true moral concerns associated with dishonest behaviour. In contrast to prior studies, we do not find groups to be more dishonest than individuals when a passive third party, such as a charity, is harmed by the dishonest behaviour. Instead, we find that groups can help to moderate the extent of dishonest behaviour. |
| Keywords: | dishonesty,group decisions,communication,social norms |
| JEL: | C91 C92 D71 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:iwqwdp:012020&r=all |
| By: | Erel Segal-Halevi; Warut Suksompong |
| Abstract: | A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired sizes and divide the cake among the groups, so that each group receives a single contiguous piece and no player finds the piece of another group better than that of the player's own group. |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2001.03327&r=all |
| By: | Blaufus, Kay; Schöndube, Jens Robert; Wielenberg, Stefan |
| Abstract: | We examine whether tax audit regimes become more efficient if (i) there are audited financial statements and (ii) tax auditors have access to the internal statutory audit report revealing information about statutory audit adjustments. Our analysis is based on a standard tax compliance game that we extend to model the strategic interaction among a firm issuing financial and tax reports, a statutory auditor, and a tax auditor. We find that the efficiency effects of additional information depend on the strength of tax auditor incentives and the weight that firms place on book income. For high-powered tax auditor incentives, we obtain no information effect on our efficiency measures. For low-powered tax auditor incentives, we find an ambiguous effect, and for mediumpowered tax auditor incentives and firms that place a high weight on book income, tax audit efficiency increases if the tax auditor has access to additional information. In the latter case, we find that granting the tax auditor access to the internal statutory audit report increases firms' tax compliance, raises tax revenues, and decreases tax audit frequency. |
| Keywords: | Tax compliance game,Tax audit,Statutory audit,Tax audit efficiency,Strategic auditing |
| JEL: | H26 M41 M42 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:arqudp:249&r=all |
| By: | Alexander Frug |
| Abstract: | The main insight of the literature on strategic information transmission is that even a small conflict of interest between a fully informed sender (e.g., a financial adviser) and an uninformed receiver (an investor) often poses considerable difficulties for effective communication. However, in many real-life situations, the sender is not fully informed at the outset but gradually studies the case before offering advice. The gradual arrival of information to the sender weakens the strategic barriers between the players and significantly improves communication. |
| JEL: | D82 D83 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1691&r=all |
| By: | Geert Ridder; Shuyang Sheng |
| Abstract: | This paper develops estimation methods for network formation models using observed data from a single large network. The model allows for utility externalities from friends of friends and friends in common, so the expected utility is nonlinear in the link choices of an agent. We propose a novel method that uses the Legendre transform to express the expected utility as a linear function of the individual link choices. This implies that the optimal link decision is that for an agent who myopically chooses to establish links or not to the other members of the network. The dependence between the agent's link choices is through an auxiliary variable. We propose a two-step estimation procedure that requires weak assumptions on equilibrium selection, is simple to compute, and has consistent and asymptotically normal estimators for the parameters. Monte Carlo results show that the estimation procedure performs well. |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2001.03838&r=all |
| By: | Shorish, Jamsheed (Shorish Research) |
| Abstract: | We present a formalization of blockchain as a state machine, focusing upon permissionless blockchains due to general audience awareness of its most popular implementation, Bitcoin (permissioned blockchains are treated similarly without loss of generality). After presenting a typical Bitcoin transaction workflow, a general blockchain state representation is derived. It is demonstrated that the proper mathematical object defining the state of a blockchain is a topological fiber bundle, because it is not possible to globally `parametrize' blocks (or ledgers of blocks) by time due to their dependence upon cryptographic hash functions. In addition, we specify a general transition function between blockchain states that is agnostic to the consensus mechanism used to write blocks into the ledger, and which is probabilistic in nature, so that blockchain may be regarded as a probabilistic state machine. We then interpret agents (both human and code-based, such as `chaincode', `smart contracts', or other artificial intelligence) as automata interacting with blockchain technology, drawing upon the theory of non-cooperative repeated interaction games. Finally, blockchain as a hierarchy of state machines is defined, and future research directions are presented using this hierarchy as a point of departure for modeling blockchain dynamics. |
| Date: | 2018–01–23 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:eusxg&r=all |
| By: | Adam Dearing; Jason R. Blevins |
| Abstract: | We propose a new sequential Efficient Pseudo-Likelihood (EPL) estimator for structural economic models with an equality constraint, particularly dynamic discrete choice games of incomplete information. Each iteration in the EPL sequence is consistent and asymptotically efficient, and iterating to convergence improves finite sample performance. For dynamic single-agent models, we show that Aguirregabiria and Mira's (2002, 2007) Nested Pseudo-Likelihood (NPL) estimator arises as a special case of EPL. In dynamic games, EPL maintains its efficiency properties, although NPL does not. And a convenient change of variable in the equilibrium fixed point equation ensures EPL iterations have the same computational simplicity as NPL iterations. Furthermore, EPL iterations are stable and locally convergent to the finite-sample maximum likelihood estimator at a nearly-quadratic rate for all regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems. Monte Carlo simulations confirm the theoretical results and demonstrate EPL's good performance in finite samples. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.10488&r=all |
| By: | Matthew Elliott; Benjamin Golub; Matthew V. Leduc |
| Abstract: | We model the production of complex goods in a large supply network. Firms source several essential inputs through relationships with other firms. Relationships may fail, and given this idosyncratic risk, firms multisource inputs and make costly investments to make relationships with suppliers stronger (less likely to fail). We find that aggregate production is discontinuous in the strength of these relationships. This has stark implications for equilibrium outcomes. We give conditions under which the supply network is endogenously fragile, so that arbitrarily small negative shocks to relationship strength lead to a large, discontinuous drop in aggregate output. |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2001.03853&r=all |
| By: | Camera, Gabriel; Hohl, Lukas (University of Basel); Weder, Rolf (University of Basel) |
| Abstract: | Standard international economic theory suggests that people should embrace economic integration because it promises large gains. But recent events such as Brexit indicate a desire for economic disintegration. Here we report results of an experiment, based on a strategic analytical framework, of how size and distribution of potential gains from integration influence outcomes and individuals' inclination to embrace integration. We find that cross-country inequality in potential gains acts as a friction to realize those gains. This suggests that to better understand recent phenomena, international economic theory should account for distributional considerations and behavioral aspects it currently ignores. |
| Keywords: | endogenous institutions, globalization, indefinitely repeated games, social dilemmas |
| JEL: | C70 C90 F02 |
| Date: | 2019–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2019/21&r=all |
| By: | Bluwstein, Kristina (Bank of England); Buckmann, Marcus (Bank of England); Joseph, Andreas (Bank of England and King’s College London); Kang, Miao (Bank of England); Kapadia, Sujit (European Central Bank); Simsek, Özgür (University of Bath) |
| Abstract: | We develop early warning models for financial crisis prediction using machine learning techniques on macrofinancial data for 17 countries over 1870–2016. Machine learning models mostly outperform logistic regression in out-of-sample predictions and forecasting. We identify economic drivers of our machine learning models using a novel framework based on Shapley values, uncovering non-linear relationships between the predictors and crisis risk. Throughout, the most important predictors are credit growth and the slope of the yield curve, both domestically and globally. A flat or inverted yield curve is of most concern when nominal interest rates are low and credit growth is high. |
| Keywords: | Machine learning; financial crisis; financial stability; credit growth; yield curve; Shapley values; out-of-sample prediction |
| JEL: | C40 C53 E44 F30 G01 |
| Date: | 2020–01–03 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0848&r=all |