|
on Game Theory |
| By: | Philippe Jehiel (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London]); Larry Samuelson (Yale University [New Haven]) |
| Abstract: | We offer an approach to cooperation in repeated games of private monitoring in which players construct models of their opponents' behavior by observing the frequencies of play in a record of past plays of the game in which actions but not signals are recorded. Players construct models of their opponent's behavior by grouping the histories in the record into a relatively small number of analogy classes to which they attach probabilities of cooperation. The incomplete record and the limited number of analogy classes lead to misspecified models that provide the incentives to cooperate. We provide conditions for the existence of equilibria supporting cooperation and equilibria supporting high payoffs for some nontrivial analogy partitions. |
| Keywords: | Analogical reasoning,Cooperation,Prisoners' dilemma,Repeated game,Private monitoring Analogical reasoning,Private monitoring |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-03754101&r= |
| By: | Daphne Cornelisse; Thomas Rood; Mateusz Malinowski; Yoram Bachrach; Tal Kachman |
| Abstract: | In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that promote long-lasting cooperation are difficult tasks. Cooperative game theory offers solution concepts identifying distribution schemes, such as the Shapley value, that fairly reflect the contribution of individuals to the performance of the team or the Core, which reduces the incentive of agents to abandon their team. Applications of such methods include identifying influential features and sharing the costs of joint ventures or team formation. Unfortunately, using these solutions requires tackling a computational barrier as they are hard to compute, even in restricted settings. In this work, we show how cooperative game-theoretic solutions can be distilled into a learned model by training neural networks to propose fair and stable payoff allocations. We show that our approach creates models that can generalize to games far from the training distribution and can predict solutions for more players than observed during training. An important application of our framework is Explainable AI: our approach can be used to speed-up Shapley value computations on many instances. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.08798&r= |
| By: | Jara-Moroni, Pedro (Universidad de Santiago de Chile.Facultad de Administración y Economía.Departamento de Economía) |
| Abstract: | In this article we prove that, when firms are identical, there are no non-degenerate mixed strategy equilibria in the linear quantity setting duopoly game studied by van Damme and Hurkens (1999) , in which firms engage in the “Action Commitment Game” proposed by Hamilton and Slutsky (1990). The consequence of this is that in the symmetric case, there can not be equilibrium selection through risk dominance in such game |
| Keywords: | Stackelberg, Cournot, Endogenous Timing, Mixed Strategies |
| JEL: | C72 D43 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:ars:papers:991943756506116&r= |
| By: | Martin Meier; Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | Heifetz, Meier and Schipper (2013) introduced generalized extensive-form games that allow for asymmetric unawareness. Here, we study the normal form of a generalized extensive-form game. The generalized normal-form game associated to a generalized extensive-form game with unawareness may consist of a collection of normal-form games. We use it to characterize extensive-form rationalizability (resp. prudent rationalizability) in generalized extensive-form games by iterative conditional strict (resp. weak) dominance in the associated generalized normal-form. We also show that the analogue to iterated admissibility for generalized normal-form games is not independent of the extensive-form structure. This is because under unawareness, a player's information set not only determines which nodes he considers possible but also of which game tree(s) he is aware of. |
| Keywords: | Awareness, unknown unknowns, extensive-form rationalizability, prudent rationalizability, iterated admissibility, iterated conditional dominance |
| JEL: | C72 D83 |
| Date: | 2022–08–30 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:351&r= |
| By: | Phillip J. K. Christoffersen; Andreas A. Haupt; Dylan Hadfield-Menell |
| Abstract: | Multi-agent reinforcement learning (MARL) is a powerful tool for training automated systems acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding state-dependent transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all fully observed Markov games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we complement our game-theoretic analysis by showing that state-of-the-art RL algorithms learn socially optimal policies given our augmentation. Our experiments include classic static dilemmas like Stag Hunt, Prisoner's Dilemma and a public goods game, as well as dynamic interactions that simulate traffic, pollution management and common pool resource management. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.10469&r= |
| By: | Robert P. Gilles; Lina Mallozzi |
| Abstract: | We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's solution conception is a bargaining solution and tries to minimise the maximal quantified "propensity to disrupt" the negotiation of the players over the allocation of the generated collective payoffs. We show that Gately's solution concept is well-defined for a broad class of games. We consider a generalisation based on a parameter-based quantification of the propensity to disrupt. Furthermore, we investigate the relationship of Gately's solution and its generalisation with the Core. We show that Gately's solution is in the Core for all regular 3-player games. We also identify precise conditions under which generalised Gately values are Core imputations for arbitrary regular cooperative games. We construct the dual of generalised Gately values and devise an axiomatisation of these values for the class of regular cooperative games. We conclude the paper with an application of the Gately value to the measurement of power in hierarchical social networks. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.10189&r= |
| By: | Denizalp Goktas; Amy Greenwald |
| Abstract: | Min-max optimization problems (i.e., min-max games) have attracted a great deal of attention recently as their applicability to a wide range of machine learning problems has become evident. In this paper, we study min-max games with dependent strategy sets, where the strategy of the first player constrains the behavior of the second. Such games are best understood as sequential, i.e., Stackelberg, games, for which the relevant solution concept is Stackelberg equilibrium, a generalization of Nash. One of the most popular algorithms for solving min-max games is gradient descent ascent (GDA). We present a straightforward generalization of GDA to min-max Stackelberg games with dependent strategy sets, but show that it may not converge to a Stackelberg equilibrium. We then introduce two variants of GDA, which assume access to a solution oracle for the optimal Karush Kuhn Tucker (KKT) multipliers of the games' constraints. We show that such an oracle exists for a large class of convex-concave min-max Stackelberg games, and provide proof that our GDA variants with such an oracle converge in $O(\frac{1}{\varepsilon^2})$ iterations to an $\varepsilon$-Stackelberg equilibrium, improving on the most efficient algorithms currently known which converge in $O(\frac{1}{\varepsilon^3})$ iterations. We then show that solving Fisher markets, a canonical example of a min-max Stackelberg game, using our novel algorithm, corresponds to buyers and sellers using myopic best-response dynamics in a repeated market, allowing us to prove the convergence of these dynamics in $O(\frac{1}{\varepsilon^2})$ iterations in Fisher markets. We close by describing experiments on Fisher markets which suggest potential ways to extend our theoretical results, by demonstrating how different properties of the objective function can affect the convergence and convergence rate of our algorithms. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.09690&r= |
| By: | Burkhard C. Schipper; Hang Zhou (Department of Economics, University of California Davis) |
| Abstract: | Level-k thinking and Cognitive Hierarchy have been widely applied as a normal-form solution concept in behavioral and experimental game theory. We consider the extension of level-k thinking to extensive-form games. Player’s may learn about levels of opponents’ thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-l thinking for l |
| Keywords: | Level-k thinking, Cognitive hierarchy, Theory-of-Mind, Rationalizability, Iterated admissibility, Extensive-form rationalizability, ∆-rationalizability, Mutual belief in rationality, Experimental game theory. |
| JEL: | C72 C92 D91 |
| Date: | 2022–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:352&r= |
| By: | Rosenmüller, Joachim (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We introduce the Maschler-Perles-Shapley value for NTU games composed by smooth bodies. This waywe extend the M-P-S value established for games composed by Cephoids (“sums of deGua Simplices”). The development is parallel to the one of the (generalized) Maschler-Perles bargaining solution. For Cephoidal bargaining problems this concept is treated in ([4], [11]). It is extended to smooth bargaining problems by the construction of surface measures. Such measures generalize the Maschler-Perles approach in two dimensions via a line integral -- what the authors call their “donkey cart” ([6], [11]). The Maschler-Perles-Shapley value for Cephoidal NTU Games extends the Cephoidal approach to Non Transferable Utility games with feasible sets consisting of Cephoids. The presentation is found in [10] and [11]. Using these results we formulate the Maschler-Perles-Shapley value for smooth NTU games. We emphasize the intuitive justification of our concepts. The original Maschler-Perles approach is based on the axiom of superadditivity which we rate much more appealing than competing axioms like IIA etc. As a consequence, the construction of a surface measure (Maschler-Perles' line integral) is instigated which renders concessions and gains of players during the bargaining process to be represented in a common space of "adjusted utility”. Within this utility space side payments -- transfer of utils -- are feasible interpersonally as well as intrapersonally. Therefore, the barycenter/midpoint of the adjusted utility space is the natural base for the solution concept. This corresponds precisely to the Maschler-Perles “donkey card” reaching the solution by calling for equal concessions in terms of their line integral. In addition, the adjusted utility space carries an obvious linear structure -- thus admitting expectations in the sense of the Shapley value or "von Neumann-Morgenstern utility". Consequently, we obtain a generally acceptable concept for bargaining problems as well as NTU games in the Cephoidal and in the smooth domain. We collect the details of this reasoning along the development of our theory in Remarks 1.7., 2.6., and 3.2.. These remarks constitute a comprehensive view on M-P-S concepts for Cephoidal and smooth NTU games. |
| Date: | 2022–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:668&r= |
| By: | Federico Navarra (University of Padova) |
| Abstract: | This paper studies the effects of price parity clauses (PPC) on consumer surplus and platform profit by investigating the strategic interactions among horizontally differentiated multi-channel retailers selling through online platforms as well as in their the direct channel. Consumers first choose which product to buy and then in which channel (online/direct) to finalize the purchase; platforms can decide about whether or not to impose PPCs. We show that the direct sales channel constrains platform pricing strategies such that PPCs have ambiguous effects on consumers. From the social welfare perspective, imposing PPCs is desirable when platforms are perceived as highly substitutable. Both platforms imposing price parity is always a Nash equilibrium but under certain conditions it can also arise another Nash equilibrium in which both platforms select an unrestricted pricing regime. |
| Keywords: | platform competition, price parity clauses, vertical restraints, showrooming, webrooming |
| JEL: | D43 L13 L42 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0281&r= |
| By: | Claudius Gros |
| Abstract: | The productivity of a common pool of resources may degrade when overly exploited by a number of selfish investors, a situation known as the tragedy of the commons (TOC). Without regulations, agents optimize the size of their individual investments into the commons by balancing incurring costs with the returns received. The resulting Nash equilibrium involves a self-consistency loop between individual investment decisions and the state of the commons. As a consequence, several non-trivial properties emerge. For $N$ investing actors we proof rigorously that typical payoffs do not scale as $1/N$, the expected result for cooperating agents, but as $(1/N)^2$. Payoffs are hence functionally reduced, a situation denoted catastrophic poverty. This occurs despite the fact that the cumulative investment remains finite when $N\to\infty$. Catastrophic poverty is instead a consequence of an increasingly fine-tuned balance between returns and costs. In addition, we point out that a finite number of oligarchs may be present. Oligarchs are characterized by payoffs that are finite and not decreasing when $N$ increases. Our results hold for generic classes of models, including convex and moderately concave cost functions. For strongly concave cost functions the Nash equilibrium undergoes a collective reorganization, being characterized instead by entry barriers and sudden death forced market exits. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.08171&r= |
| By: | Dai ZUSAI |
| Abstract: | In this note, we consider dynamically optimal pricing of a network good, when consumers' demand adjusts only gradually. We find a Lyapunov function that characterizes where and how the platform size converges under the dynamically optimal pricing. Given the current platform size, we compare the value of the Lyapunov function with the profit under static pricing that keeps this current size at a Nash equilibrium of consumers' entry game. We show that the difference between them can be interpreted as adjustment costs and we justify this interpretation by regarding a myopic pricing scheme as an approximation. This justification suggests that recurrent adjustment of the myopic pricing scheme brings the platform to the same size in the long run as the dynamically optimal pricing. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:toh:tupdaa:23&r= |
| By: | Claus-Jochen Haake (Paderborn University); Martin Schneider (Paderborn University) |
| Abstract: | Qualitative comparative analysis (QCA) enables researchers in international management to better understand how the impact of a single explanatory factor depends on the context of other factors. But the analytical tool box of QCA does not include a parameter for the explanatory power of a single explanatory factor or “condition†. In this paper, we therefore reinterpret the Banzhaf power index, originally developed in cooperative game theory, to establish as a goodness-of-fit parameter in QCA. The relative Banzhaf index we suggest measures the explanatory power of one condition averaged across all sufficient combinations of conditions. The paper argues that the index is especially informative in three situations that are all salient in international management, namely substantial limited diversity in the data, the emergence of strong INUS conditions in the analysis, and theorizing with contingency factors. The paper derives the properties of the relative Banzhaf index in the QCA context, demonstrates how the index can be computed easily from a rudimentary truth table, and explores its insights by revisiting selected papers in international management that apply fuzzy-set QCA. The discussion section offers routes for exploring further how the relative Banzhaf and other power indexes can be applied in QCA. |
| Keywords: | Qualitative comparative analysis, Banzhaf power index, causality, explanatory power |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:150&r= |
| By: | Marianne Guillet; Maximilian Schiffer |
| Abstract: | Current electric vehicle market trends indicate an increasing adoption rate across several countries. To meet the expected growing charging demand, it is necessary to scale up the current charging infrastructure and to mitigate current reliability deficiencies, e.g., due to broken connectors or misreported charging station availability status. However, even within a properly dimensioned charging infrastructure, a risk for local bottlenecks remains if several drivers cannot coordinate their charging station visit decisions. Here, navigation service platforms can optimally balance charging demand over available stations to reduce possible station visit conflicts and increase user satisfaction. While such fleet-optimized charging station visit recommendations may alleviate local bottlenecks, they can also harm the system if self-interested navigation service platforms seek to maximize their own customers' satisfaction. To study these dynamics, we model fleet-optimized charging station allocation as a resource allocation game in which navigation platforms constitute players and assign potentially free charging stations to drivers. We show that no pure Nash equilibrium guarantee exists for this game, which motivates us to study VCG mechanisms both in offline and online settings, to coordinate players' strategies toward a better social outcome. Extensive numerical studies for the city of Berlin show that when coordinating players through VCG mechanisms, the social cost decreases on average by 42 % in the online setting and by 52 % in the offline setting. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.09530&r= |
| By: | Francesco Giovannoni; Toomas Hinnosaar |
| Abstract: | We study a buyer-seller problem of a novel good for which the seller does not yet know the production cost. A contract can be agreed upon at either the ex-ante stage, before learning the cost, or at the ex-post stage, when both parties will incur a costly delay, but the seller knows the production cost. We show that the optimal ex-ante contract for a profit-maximizing seller is a fixed price contract with an "at-will" clause: the seller can choose to cancel the contract upon discovering her production cost. However, sometimes the seller can do better by offering a guaranteed-delivery price at the ex-ante stage and a second price at the ex-post stage if the buyer rejects the first offer. Such a "limited commitment" mechanism can raise profits, allowing the seller to make the allocation partially dependent on the cost while not requiring it to be embedded in the contract terms. Analogous results hold in a model where the buyer does not know her valuation ex-ante and offers a procurement contract to a seller. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.04985&r= |
| By: | Rangeet Bhattacharyya; Palash Dey; Swaprava Nath |
| Abstract: | The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information of the auction is available to every participant, Myerson [17] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [10, 15]) were designed that appropriately incentivize the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this larger class of randomized auctions. We obtain the structure of the revenue optimal auction for i.i.d. bidders on arbitrary trees. We discuss the possibilities of addressing more general settings. Through experiments, we show that auctions following this characterization can provide a higher revenue than the currently known auctions on networks. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.09326&r= |
| By: | Ali Hortaçsu; Aniko Oery; Kevin R. Williams |
| Abstract: | We introduce a model of oligopoly dynamic pricing where firms with limited capacity face a sales deadline. We establish conditions under which the equilibrium is unique and converges to a system of differential equations. Using unique and comprehensive pricing and bookings data for competing U.S. airlines, we estimate our model and find that dynamic pricing results in higher output but lower welfare than under uniform pricing. Our theoretical and empirical findings run counter to standard results in single-firm settings due to the strategic role of competitor scarcity. Pricing heuristics commonly used by airlines increase welfare relative to estimated equilibrium predictions. |
| JEL: | C70 C73 D21 D22 D43 D60 L13 L93 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30347&r= |
| By: | Philippe Jehiel (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London]); Erik Mohlin (Lund University [Lund], Institute for Futures Studies) |
| Abstract: | We study learning in a decentralized pairwise adverse selection economy, where buyers have access to the quality of traded goods but not to the quality of nontraded goods. Buyers categorize ask prices in order to predict quality as a function of ask price. The categorization is endogenously determined so that outcomes that are observed more often are categorized more finely, and within each category beliefs reflect the empirical average. This leads buyers to have a very fine understanding of the relationship between qualities and ask prices for prices below the current market price, but only a coarse understanding above that price. We find that this induces a price cycle involving the Nash equilibrium price, and one or more higher prices. |
| Keywords: | Adverse selection,Bounded rationality,Categorization,Learning,Model misspeciÖcation,OTC markets Adverse selection,Model misspecification,OTC markets |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-03754118&r= |
| By: | Kohei Daido (Kwansei Gakuin University); Tomoya Tajika (Nihon University) |
| Abstract: | This study develops a dynamic model of information projection and explores how it affects timing of actions. An action is observable and available only after the agents' arrival. The value of an action is unknown; however, each agent receives a noisy signal on its value. Without information projection, if no one has taken action until then, the expected value of taking action reduces with the passage of time because inaction is a bad signal. In contrast, under projection bias, because of which the agent mistakenly believes that the other agent's arrival time is close to theirs, the expected action value may increase as time passes. Consequently, the agent has second thoughts; although they decide not to take action when they find the problem, they overturn their initial decision and take action later. |
| Keywords: | Delay, Information projection bias, Preemption games, Second thoughts, Social learning |
| JEL: | D81 D82 D83 D91 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:238&r= |
| By: | Anindya Bhattacharya |
| Abstract: | In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is bounded). One novelty of this exercise is that our domain is the {\em entire} class of such games: i.e., restrictions like "non-levelness" or "balancedness" are not required. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.01690&r= |
| By: | Georg Kirchsteiger; Tom Lenaerts; Remi Suchon |
| Abstract: | In sequential social dilemmas with stranger matching, initiating cooperation is inherently risky for the first mover. The disclosure of the second mover’s past actions may be necessary to instigate cooperation. We experimentally compare the effect of mandatory and voluntary disclosure with non disclosure in a sequential prisoner’s dilemma situation. Our results confirm the positive effects of disclosure on cooperation. We also find that voluntary disclosure is as effective as mandatory one, which is surprising given the results of existing literature on this topic. With voluntarydisclosure, second movers with a good track record decided to disclose because they expect that not disclosing signals non-cooperativeness. First movers interpret nondisclosure correctly as a signal of non-cooperativeness. Therefore, they cooperate less than half as often when the second mover does not disclose. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/348594&r= |
| By: | Howard Kunreuther; Artem Demidov; Mark Pauly; Matija Turcic; Michael Wilson |
| Abstract: | Much of the property damage from wildfires occurs when fires spread into built up areas, the wildland urban interface. Fire spread within such areas occurs from house to house, as embers from one burning structure ignite neighboring ones. Actions can be taken to mitigate the chances that a given house will ignite. This size and configuration of this external benefit depends on the assumed process of fire spread. In this paper we use a simulation model based on plausible parameters to illustrate likely patterns of marginal benefit from mitigation as a function of building density and effectiveness of mitigation. The model indicates that a common pattern is for marginal benefit to unmitigated neighbors to be low at low levels of community mitigation, rise to a maximum, and then fall quickly to a low level. This maximum marginal benefit (known as “herd immunity”) helps to indicate the optimal pattern of mitigation in a community. However individual owners in Nash equilibrium will not take the spillover benefits into account. We use the distribution of house values in a California community relative to an assumed cost of mitigation to illustrate in the model the level of mitigation owners will undertake when they make independent investment decisions, and the corrective actions that can lead to the social optimum. We discuss the use of rules or subsidies for insurance premium adjustments based on mitigation activities. Because it will rarely be optimal to mitigate all homes, the optimal solution may involve unequal treatment and raise equity issues. |
| JEL: | H0 Q0 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30348&r= |
| By: | Antelo, Manel; Bru, Lluís |
| Abstract: | In a differentiated Stackelberg duopoly, we explore the licensing behaviour of an inside patent holder owning a cost-reducing innovation and that may play as a leader or follower in setting the output level in the marketplace. We find that, regardless of whether the licensor is the leader or the follower, the licensing contract always involves royalties: per-unit or ad-valorem (depending on the degree of product differentiation and the size of the innovation) when the licensor is the leading firm, and per-unit royalties (alone or combined with a fixed payment) when it is the follower. We also show that, as compared to the pre-licensing context, licensing by a market follower is never welfare reducing, and licensing by a market leader is only welfare reducing when the products are very close substitutes. |
| Keywords: | Stackelberg industry, licensing, differentiated products, per-unit and ad-valorem royalties, welfare |
| JEL: | L13 L24 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:114181&r= |
| By: | Alger, Ingela |
| Abstract: | The 50-year old definition of an evolutionarily stable strategy provided a key tool for theorists to model ultimate drivers of behavior in social interactions. For decades economists ignored ultimate drivers and used models in which individuals choose strate-gies based on their preferences. This article summarizes some key findings in the literature on evolutionarily stable preferences, which in the past three decades has proposed models that combine the two approaches: Nature equips individuals with preferences, which deter-mine their strategy choices, which in turn determines evolutionary success. The objective is to highlight complementarities and potential avenues for future collaboration between biologists and economists. |
| Date: | 2022–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:tse:iastwp:127262&r= |