Game Theory
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Game Theory
2017-08-06
Coalition Formation and History Dependence
http://d.repec.org/n?u=RePEc:wrk:wcreta:33&r=gth
Farsighted formulations of coalitional formation, for instance by Harsanyi (1974) and Ray and Vohra(2015), have typically been based on the von Neumann- Morgenstern (1944) stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional ‘moves’ in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra(2016) point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra (2016) restricted coalitions to hold common, history independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta-Vohra analysis by allowing for history dependent expectations. The paper provides characterization results for two solution concepts corresponding to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.
Dutta, Bhaskar
Vartiainen, Hannu
2017
Endogenous Mergers in Markets with Vertically Diffeerentiated Products
http://d.repec.org/n?u=RePEc:pra:mprapa:80528&r=gth
This paper studies the incentives of firms selling vertically differentiated products to merge. To this aim, we introduce a three-stage game in which, at the first stage, three independent firms can decide to merge with their competitors via a sequential game of coalition formation and, at the second and third stage, they can optimally revise their qualities and prices, respectively. We study whether such binding agreements (i.e. full or partial mergers) can be sustained as subgame perfect equilibria of the coalition formation game, and analyze their effects on equilibrium qualities, prices and profits. We find that, although profitable, the merger-to-monopoly of all firms is not an outcome of the finite-horizon negotiation, where only partial mergers arise. Moroever, we show that all stable mergers always include the firm initially producing the bottom quality good and reduce the number of variants on sale.
Jaskold Gabszewicz, Jean
Marini, Marco A.
Tarola, Ornella
Mergers, Price Collusion, Vertically Differentiated Products, Sequential Game of Coalition Formation.
2017-07-20
US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality
http://d.repec.org/n?u=RePEc:has:discpr:1716&r=gth
To ensure equal representation, the voting districts of a country must be more or less of the same size. Designing such voting districts, however, is not an easy task due to the fact that voting districts are encompassed in administrative regions. Since the respective share of an administrative region, i.e.\ the number of seats its entitled to based on its population, is not necessarily an integer number, it is hard to distribute the seats in a fair way. The arising fair distribution problem is called the apportionment problem. Proportionality of the allocation is the most important, but not the only factor of a fair solution. Monotonicity related difficulties, administrative and demographic issues make the problem more complex. We provide an overview of the classical apportionment methods as well as the Leximin Method – a new apportionment technique designed to comply with the recommendation made by the Venice Commission. We discuss the properties of apportionments and test the most prominent methods on real data.
Laszlo A. Koczy
Peter Biro
Balazs Sziklai
Apportionment problem, Largest remainder methods, Divisor methods, Venice Commission, Leximin method
2017-06
A sequential bargaining protocol for land rental arrangements
http://d.repec.org/n?u=RePEc:pra:mprapa:80424&r=gth
We consider land rental between a single tenant and several lessors. The tenant should negotiate sequentially with each lessor for the available land. In each stage, we apply the Nash bargaining solution. Our results imply that, when all land is necessary, a fixed price per unit is more favourable for the tenant than a lessor-dependent price. Furthermore, a lessor is better off with a lessor-dependent price only when negotiating first. For the tenant, lessors' merging is relevant with lessor-dependent price but not with fixed price.
Valencia-Toledo, Alfredo
Vidal-Puga, Juan
Bargaining; non-cooperative game; Nash solution; land rental
2017-07-25
Control-stopping Games for Market Microstructure and Beyond
http://d.repec.org/n?u=RePEc:arx:papers:1708.00506&r=gth
In this paper, we present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. A distinctive feature of this family of games is the fact that the agents do not have any exogenously given fundamental value for the asset, and they deduce the value of their position from the bid and ask prices posted by other agents (i.e. they are pure speculators). As a result, in such a game, the reward function of each agent, at the time of stopping, depends directly on the controls of other players. The equilibrium problem leads naturally to a system of coupled control-stopping problems (or, equivalently, Reflected Backward Stochastic Differential Equations (RBSDEs)), in which the individual reward functions (or, reflecting barriers) depend on the value functions (or, solution components) of other agents. The resulting system, in general, presents multiple mathematical challenges due to the non-standard form of coupling (or, reflection). In the present case, this system is also complicated by the fact that the continuous controls of the agents, describing their posted bid and ask prices, are constrained to take values in a discrete grid. The latter feature reflects the presence of a positive tick size in the market, and it creates additional discontinuities in the agents reward functions (or, reflecting barriers). Herein, we prove the existence of a solution to the associated system in a special Markovian framework, provide numerical examples, and discuss the potential applications.
Roman Gayduk
Sergey Nadtochiy
2017-08
Stable Marriage With and Without Transferable Utility:Nonparametric Testable Implications
http://d.repec.org/n?u=RePEc:eca:wpaper:2013/255694&r=gth
We show that transferable utility has no nonparametrically testable implications for marriage stability in settings with a single consumption observation per house- hold and heterogeneous individual preferences across households. This completes the results of Cherchye, Demuynck, De Rock, and Vermeulen (2017), who characterized Pareto efficient household consumption under the assumption of marriage stability without transferable utility. First, we show that the nonparametric testable conditions established by these authors are not only necessary but also sufficient for rationalizability by a stable marriage matching. Next, we demonstrate that exactly the same testable implications hold with and without transferable utility between household members. We build on this last result to provide a primal and dual linear programming characterization of a stable matching allocation for the observational setting at hand. This provides an explicit specification of the marital surplus function rationalizing the observed matching behavior.
Laurens Cherchye
Thomas Demuynck
Bram De Rock
Frederic Vermeulen
marriage stability; household consumption; nonparametric testable implications; transferable utility
2017-07
Providing Efficient Network Access to Green Power Generators : A Long-term Property Rights Perspective
http://d.repec.org/n?u=RePEc:tiu:tiutil:f70cf82e-fedd-4e68-8e8f-a189636fd474&r=gth
Coordinating the timing of new production facilities is one of the challenges of liberalized power sectors. It is complicated by the presence of transmission bottlenecks, oligopolistic competition and the unknown prospects of low-carbon technologies. We build a model encompassing a late and early investment stage, an existing dirty (brown) and a future clean (green) technology and a single transmission bottleneck, and compare dynamic efficiency of several market designs. Allocating network access on a short-term competitive basis distorts investment decisions, as brown firms will preempt green competitors by investing early. Dynamic efficiency is restored with long-term transmission rights that can be traded on a secondary market. We show that dynamic efficiency does not require the existence of physical rights for accessing the transmission line, but financial rights on receiving the scarcity revenues generated by the transmission line suffice.
Petropoulos, G.
Willems, Bert
network access; congestion management; renewable energy sources; power markets
2017
Symmetric multi-person zero-sum game with two sets of strategic variables
http://d.repec.org/n?u=RePEc:pra:mprapa:75838&r=gth
We consider a symmetric multi-person zero-sum game with two sets of alternative strategic variables which are related by invertible functions. They are denoted by (s1, s2, ..., sn) and (t1, t2, ..., tn) for players 1, 2, ..., n. The number of players is larger than two. We consider a symmetric game in the sense that all players have the same payoff functions. We do not postulate differentiability of the payoff functions of players. We will show that the following patterns of competition, 1) all players choose si, 2) all players choose ti and 3) m players choose ti, i=1, ..., m and n-m players choose sj, j=m+1, ..., n where 1
Satoh, Atsuhiro
Tanaka, Yasuhito
multi-person zero-sum game, two strategic variables
2016-12-28
The Bitcoin Mining Game: On the Optimality of Honesty in Proof-of-work Consensus Mechanism
http://d.repec.org/n?u=RePEc:chc:wpaper:0060&r=gth
We consider a game in which Bitcoin miners compete for a reward of each solved puzzle in a sequence of them. We model it as a sequential game with imperfect information, in which miners have to choose whether or not to report their success. We show that the game has a multiplicity of equilibria and we analyze the parameter constellations for each of them. In particular, the minimum requirement to find it optimal not to report is decreasing with the number of miners who are not reporting, and increasing the heterogeneity among players reduces the likelihood that they choose not to report.
Juan Beccuti
Christian Jaag
Bitcoin, Mining, Proof of work, Game theory
2017-08
Efficient Public Good Provision in Networks : Revisiting the Lindahl Solution
http://d.repec.org/n?u=RePEc:fip:fedgif:1210&r=gth
The provision of public goods in developing countries is a central challenge. This paper studies a model where each agent’s effort provides heterogeneous benefits to the others, inducing a network of opportunities for favor-trading. We focus on a classical efficient benchmark – the Lindahl solution – that can be derived from a bargaining game. Does the optimistic assumption that agents use an efficient mechanism (rather than succumbing to the tragedy of the commons) imply incentives for efficient investment in the technology that is used to produce the public goods? To show that the answer is no in general, we give comparative statics of the Lindahl solution which have natural network interpretations. We then suggest some welfare-improving interventions.
Anil K. Jain
Networks ; Public goods ; β-core ; Repeated games ; Coalitional deviations ; Institutions ; Centrality ; Lindahl equilibrium
2017-07-28
Behavioral Patterns in Conditional Generosity Experiments
http://d.repec.org/n?u=RePEc:lui:cesare:1701&r=gth
Conditional generosity is explored experimentally by confronting two participants with the same allocation task and allowing only one of them to adjust the own generosity level via conditioning on whether the other intends to be more, respectively less generous. Only one of two allocator candidates can actually give conditioning on the other’s intended generosity to the respective responder. We employ the strategy vector method but restrict conditioning to qualitative information only. The focus is on how generosity inclinations, largely responsible for fair(er) allocation results and charitable giving, are affected by information that one anonymous other just intended to be more, respectively less generous. Participants play three successive games in the order ultimatum, yes-no and impunity game or (between subjects) in the reversed order. Although only impunity appeals to intrinsic generosity intentions, we test whether conditioning persists when sanctioning is possible. Based on our data, we distinguish two major types of participants, one yielding to weakest social influence and another immune to it. The latter type offers much less: it is greed which, as expected, weakens social influence.
Daniela Di Cagno
Arianna Galliera
Werner Güth
Luca Panaccione
(Conditional) Generosity, Ultimatum Game, Yes-No Game, Impunity Game, Experiments.
Core Existence in Vertically Differentiated Markets
http://d.repec.org/n?u=RePEc:pra:mprapa:80426&r=gth
We prove that a sufficient condition for the core existence in a n-firm vertically differentiated market is that the qualities of firms' products are equispaced along the quality spectrum. This result contributes to see that a fully collusive agreement among firms in such markets is more easily reachable when product qualities are not distributed too asymmetrically along the quality ladder.
Gabszewicz, Jean
Marini, Marco A.
Tarola, Ornella
Vertically Differentiated Markets; Price Collusion; Core; Grand Coalition; Coalition Stability; Games with Externalities; Partition Function Games.
2016-12-10
Nash equilibria for game contingent claims with utility-based hedging
http://d.repec.org/n?u=RePEc:arx:papers:1707.09351&r=gth
Game contingent claims (GCCs) generalize American contingent claims by allowing the writer to recall the option as long as it is not exercised, at the price of paying some penalty. In incomplete markets, an appealing approach is to analyze GCCs like their European and American counterparts by solving option holder's and writer's optimal investment problems in the underlying securities. By this, partial hedging opportunities are taken into account. We extend results in the literature by solving the stochastic game corresponding to GCCs with both continuous time stopping and trading. Namely, we construct Nash equilibria by rewriting the game as a non-zero-sum stopping game in which players compare payoffs in terms of their exponential utility indifference values. As a by-product, we also obtain an existence result for the optimal exercise time of an American claim under utility indifference valuation by relating it to the corresponding nonlinear Snell envelope.
Klebert Kentia
Christoph K\"uhn
2017-07
Partition Equilibria in a Japanese-English Auction with Discrete Bid Levels for the Wallet Game
http://d.repec.org/n?u=RePEc:wrk:wcreta:34&r=gth
We consider the set-up of a Japanese-English auction with exogenously fi xed discrete bid levels for the wallet game with two bidders, following Gonçalves and Ray (2017). We show that in this auction, partition equilibria exist that may be separating or pooling. We illustrate some separating and pooling equilibria with two and three discrete bid levels. We also compare the revenues of the seller from these equilibria and thereby nd the optimal choices of bid levels for these cases.
Gonçalves, Ricardo
Ray, Indrajit
Japanese-English auctions ; wallet game ; discrete bids, partitions ; pooling equilibrium; separating equilibrium. JEL classification numbers: C72 ; D44
2017
Incentivized Kidney Exchange
http://d.repec.org/n?u=RePEc:boc:bocoec:931&r=gth
Within the last decade, kidney exchange has become a mainstream paradigm to increase the number of transplants. However, compatible pairs do not participate, and the full benefits from exchange can be realized only if they do. In this paper, we propose a new scheme, incentivizing participation of compatible pairs in exchange via insurance for a future renal failure in the patient. Efficiency and equity analyses of this scheme are conducted and compared with that of living-donor exchange in a new dynamic continuum model of kidney transplantation. We also calibrate the model with data from the US and quantify our predictions.
Tayfun Sönmez
M. Utku Ünver
M. Bumin Yenmez
Market design, organ allocation, kidney exchange, equity, efficiency, compatible pairs
2017-06-30
Networks, Frictions, and Price Dispersion
http://d.repec.org/n?u=RePEc:red:sed017:331&r=gth
This paper studies price dispersion in buyer-seller markets using networks to model frictions, where buyers are linked with a subset of sellers and sellers are linked with a subset of buyers. Our approach allows for indirect competition, where a buyer who is not directly linked with a seller affects the price obtained by that seller. Indirect competition generates the central finding of our paper: price dispersion depends on both the number of links in the network and the structure of the network (how links are distributed). Networks with very few links can have no price dispersion, while networks with many links can still support significant price dispersion. We develop a decomposition of the network that characterizes which links are redundant (i.e. have no effect on prices). We show that a particular network structure (Hamiltonian Cycle) with only two links per node has no price dispersion. We then use a theorem from Frieze (1985) to show that this network structure arises asymptotically with probability one in a randomly drawn network, even as the probability of an individual link goes to zero. We also show the finite sample properties of this relationship and find that even small sparse networks can have very little price dispersion. In an application to eBay, we show that our model reproduces the price dispersion seen in the data quite well, and that 35-45 percent of the price dispersion at eBay can be explained by the network structure alone.
Pablo Schenone
Gregory Veramendi
Javier Donna
2017