The Continuous Hotelling Pure Location Game with Elastic Demand Revisited
Mouche, Pierre von - \ 2020
In: Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Proceedings. - Springer (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ) - ISBN 9783030499877 - p. 246 - 262.
Hotelling game - Potential game - Principle of Minimum Differentiation - Pure Nash equilibrium existence
The Hotelling pure location game has been revisited. It is assumed that there are two identical players, strategy sets are one-dimensional, and demand as a function of distance is constant or strictly decreasing. Besides qualitative properties of conditional payoff functions, attention is given to the structure of the equilibrium set, best-response correspondences and the existence of potentials.
Securing land rights under rapid population growth: The feasibility of institutional land rights protection in Africa
Haagsma, R. ; Mouche, P.H.M. van - \ 2020
Journal of Institutional and Theoretical Economics 176 (2020)2. - ISSN 0932-4569 - p. 312 - 350.
The paper examines the claim that a virtuous cycle of more secure land rights, more land-saving investments, and denser populations requires the development of institutions that regulate competition over land. We construct a contest model that links the tenure-security-investment relationship to the efforts of land users to enhance land rights themselves and the role of institutional protection. We study the effect of population growth on a close-to-subsistence economy, including the possibility that it weakens institutional protection. We derive sufficient conditions for a positive effect on land investment, but also show that population growth can push the economy into a low-productivity trap.
The two-stage game approach to coalition formation: Where we stand and ways to go
Hagen, Achim ; Mouche, Pierre von; Weikard, Hans Peter - \ 2020
Games 11 (2020)1. - ISSN 2073-4336
Binary action game - Cartel game - Coalition formation - Cournot-like game - Equilibrium coalition structure - Potential game - Symmetric game - Two-stage game
Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used approach for the case where actions are simultaneous in each stage. Herein, we give special attention to the case of a symmetric physical game. Various theoretical results, in particular, for cartel games, are provided. As they are crucial, recent results on the uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives.
Cournot Equilibrium Uniqueness: At 0 Discontinuous Industry Revenue and Decreasing Price Flexibility
Mouche, Pierre Von; Sato, Takashi - \ 2019
International game theory review (2019). - ISSN 0219-1989
Cournot oligopoly - decreasing price flexibility - discontinuous payoff functions - equilibrium uniqueness - pseudo-concavity - Selten-Szidarovszky technique
We consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and a proper price function p with decreasing price flexibility. This class allows for (at 0) discontinuous industry revenue and in particular for p (y) = y-α. The paper illustrates in an exemplary way the Selten-Szidarovszky technique based on virtual backward reply functions. An algorithm for the calculation of the unique equilibrium is provided.
Binary action games : Deviation properties, semi-strict equilibria and potentials
limura, Takuya ; Mouche, Pierre von; Watanabe, Takahiro - \ 2018
Discrete Applied Mathematics 251 (2018). - ISSN 0166-218X - p. 57 - 68.
Binary action game - Cartel game - Internal and external stability - Market entry game - Nash equilibrium - Potential game - Symmetric game
For binary action games we present three properties which have in common that they are defined by conditions on marginal payoffs. The first two properties guarantee the existence of a special type of Nash equilibrium called semi-strict Nash equilibrium, for which we also show an algorithm to locate. The third one guarantees the existence of an exact potential, and can realize the aforementioned two properties in a class of exact potential games. The first one guarantees the existence of a generalized ordinal potential. Each symmetric binary action game possesses all the three properties. The results are illustrated by three applications.
Cournot tatonnement and Nash equilibrium in binary status games
Kukushkin, Nikolai S. ; Mouche, Pierre von - \ 2018
Economics Bulletin 38 (2018)2. - ISSN 1545-2921 - p. 1038 - 1044.
We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property," are established.
Groundwater flow and heat transport for systems undergoing freeze-thaw : Intercomparison of numerical simulators for 2D test cases
Grenier, Christophe ; Anbergen, Hauke ; Bense, Victor ; Chanzy, Quentin ; Coon, Ethan ; Collier, Nathaniel ; Costard, François ; Ferry, Michel ; Frampton, Andrew ; Frederick, Jennifer ; Gonçalvès, Julio ; Holmén, Johann ; Jost, Anne ; Kokh, Samuel ; Kurylyk, Barret ; McKenzie, Jeffrey ; Molson, John ; Mouche, Emmanuel ; Orgogozo, Laurent ; Pannetier, Romain ; Rivière, Agnès ; Roux, Nicolas ; Rühaak, Wolfram ; Scheidegger, Johanna ; Selroos, Jan Olof ; Therrien, René ; Vidstrand, Patrik ; Voss, Clifford - \ 2018
Advances in Water Resources 114 (2018). - ISSN 0309-1708 - p. 196 - 218.
Code benchmarking - Numerical simulation - Permafrost - Sharp interface problems - Thermo-hydrological coupling
In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. This issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatial and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.
The Hotelling bi-matrix game
Mouche, P.H.M. van; Pijnappel, Willem - \ 2018
Optimization Letters 12 (2018)1. - ISSN 1862-4472 - p. 187 - 202.
bi-matrix game - demi-modality - hotelling - location theory - nash equilibrium - tarski fixed point theorem
We study the pure equilibrium set for a specific symmetric finite game in strategic form, referred to as the Hotelling bi-matrix game. General results tha guarantee non-emptiness of this set (for all parametric values) do not seem to exist. We prove non-emptiness by determining the pure equilibrium set. In this proof so-called demi-modality properties of the conditional payoff functions play an important role.
Best-response potential for Hotelling pure location games
Iimura, Takuya ; Mouche, Pierre van; Watanabe, Takahiro - \ 2017
Economics Letters 160 (2017). - ISSN 0165-1765 - p. 73 - 77.
Best-response potential games - Location games - Pure Nash equilibrium existence - Symmetric games
We revisit two-person one-dimensional pure location games à la Anderson et al. (1992) and show that they admit continuous best-response potential functions (Voorneveld, 2000) if demand is sufficiently elastic (to the extent that the Principle of Minimum Differentiation fails); if demand is not that elastic (or is completely inelastic) they still admit continuous quasi-potential functions (Schipper, 2004). We also show that, even if a continuous best-response potential function exists, a generalized ordinal potential function (Monderer and Shapley, 1996) need not exist.
The selten–szidarovszky technique : The transformation part
Mouche, Pierre von - \ 2016
In: Recent Advances in Game Theory and Applications / Petrosyan, L.A., Mazalov, V.V., Birkhauser (Static and Dynamic Game Theory: Foundations and Applications ) - ISBN 9783319438375 - p. 147 - 164.
Aggregative games - Fixed points - Nash equilibria - Selten-Szidarovszky technique
A technique due to Selten and Szidarovszky for the analysis of Nash equilibria of games with an aggregative structure is reconsidered. Among other things it is shown that the transformation part of this technique can be extended to abstract games with co-strategy mappings and allows for a purely algebraic setting.
On the Endowment Effect in "Apple-Mars" Experiments
Haagsma, R. ; Mouche, P.H.M. van - \ 2016
APSTRACT: Applied Studies in Agribusiness and Commerce 10 (2016)2-3. - ISSN 1789-221X - p. 47 - 50.
In this article we take a close look at a specific type of behavioural experiment concerning the endowment effect. We argue that if such experiments ignore to test for the presence of persons in the sample who are indifferent between alternatives, the identification procedure for establishing an endowment effect is fallible.
|The Selten-Szidarovsky Technique: the Transformation Part
Mouche, P.H.M. van - \ 2016
In: Recent Advances in Game Theory and Applications / Petrosyan, Leon A., Mazalov, Vladimir V., Birkhauser - ISBN 9783319438382
A technique due to Selten and Szidarovszky for the analysis of Nash equilibria of games with an aggregative structure is reconsidered. Among other things it is shown that the transformation part of this technique can be extended to abstract games with co-strategy mappings and tha this part allows for a porely algebraic setting.
On the Geometric Structure of the Cournot Equilibrium Set: the Case of Concave Industry Revenue and Convex Costs
Mouche, P.H.M. van; Quartieri, F. - \ 2016
In: Equilibrium Theory for Cournot Oligopolies and Related Games Springer - p. 63 - 88.
The recent results in von Mouche and Quartieri (Econ Bull 35(2):1299-1305, 2015) on equilibrium (semi-)-uniqueness for homogeneous Cournot oligopolies with concave industry revenu and convex costs are refined and conceptualised. For this class of oligopolies also new results concerning the geometric structure of the equilibrium set E are provided. In particular, a subclass is identified for wich E is a non-empty polytope on which the equilibrium aggregator is constant and a subclass for which e i a 1-dimensional polytope on which the equilibrium aggregator is injective.
Equilibrium Theory for Cournot Oligopolies and Related Games : Essays in Honour of Koji Okuguchi
Mouche, P.H.M. van; Quartieri, Federico - \ 2016
Springer International Publishing (Springer Series in Game Theory ) - ISBN 9783319292533 - 279 p.
This state-of-the-art collection of papers on the theory of Cournotian competition focuses on two main subjects: oligopolistic Cournot competition and contests. The contributors present various applications of the Cournotian Equilibrium Theory, addressing topics such as equilibrium existence and uniqueness, equilibrium structure, dynamic processes, coalitional behavior and welfare. Special emphasis is placed on the aggregative nature of the games that are relevant to such theory. This contributed volume was written to celebrate the 80th birthday of Prof. Koji Okuguchi, a pioneer in oligopoly theory.
|Interconnected Games and International Environmental Problems
Mouche, P.H.M. van; Folmer, H. ; Ragland, S. - \ 2015
In: Game theory and International Environmental Cooperation / Finus, M., Caparros, A., Cheltenham, U.K. : Edgar Elgar Publishing (The International Library of Critical Writings in Economics series ) - ISBN 9781782545095 - p. 215 - 237.
The purpose of this paper to introduce the concept of interconnected games and to show its relevance for modeling international environmental problems. It is argued that an interconnected game approach to international environmental problems may enhance cooperation and provide an alternative to the use of financial side payments to induce countries to cooperate. Two types of interconnected games are distinguished in this paper, i.e. direct sum games and tensor games. In the former all the constituting isolated games are games in a strategic form and in the latter they are repeated games. In both cases the interconnected game can be interpreted as a multiple objective game, but only the setting where a trade-off is made for the vector-payoffs is considered. In additin to the formal definition of these types of interconnected games, some elemenary results concerning Nash equilibria of such games are derived.
Nash Equilibria of Transboundary Pollution Games
Folmer, H. ; Mouche, P.H.M. van - \ 2015
In: Handbook of Research methods and Applications in Environmental Studies / Ruth, Matthias, Cheltenham, UK : Edward Elgar (Handbooks of Research Methods and Applications series ) - ISBN 9781783474639 - p. 504 - 524.
We reconsider the Nash equilibrium existence and uniqueness problem for transboundary pollution games. There is special attention for the equilibrium set E for effective compact transboundary pollution games with continuous strictly concave production functions, continuous convex damage cost functions and uniformly distributed transboundary pollution. For this case we show that E is a non-empty polytope and that for each country all equilibrium deposition levels are equal. If in addition each damage cost function is differentiable, then there is a unique equilibrium. The results are obtained by exploiting the aggregative structure of transboundary pollution games.
Floquet theory and economic dynamics II
Heijman, W.J.M. ; Mouche, P.H.M. van - \ 2015
- 59 p.
Floquet theory is an appropriate tool for studying ordinary linear recurrence and differential equations with periodic coefficients, and is a generalization of the theory for constant coefficients. Floquet theory has still not found its way into economics, although it seems to be relevant for economic dynamics. As well as a discussion of this relevance and an illustration of it in the context of the Samuelson-Hicks multiplier-accelerator model, this article contains an appendix that provides a quite complete exposition of Floquet theory for recurrence equations.
Return of the icecream men. A discrete hotelling game
Abudaldah, Nabi ; Heijman, W.J.M. ; Heringa, Pieter ; Mouche, P.H.M. van - \ 2015
Romanian Journal of Regional Science 9 (2015)2. - ISSN 1843-8520 - p. 39 - 48.
discrete Hotelling game - Maple - Nash equilibrium
We consider a finite symmetric game in strategic form between two players which can be interpreted as a discrete variant of the Hotelling game in a one or two-dimensional space. As the analytical investigation of this game is tedious, we simulte with Maple and formulate some conjectures. In addition we present a short literature overview.
Cournot equilibrium uniqueness in case of concave industry revenue : A simple proof
Mouche, Pierre van; Quartieri, Federico - \ 2015
Economics Bulletin 35 (2015)2. - ISSN 1545-2921 - p. 1299 - 1305.
A simple proof of an equilibrium uniqueness result by Murphy, Sherali and Soyster for homogeneous Cournot oligopolies with concave industry revenue function and convex cost functions is provided. Adapting this proof, a substantial improvement of their result is obtained; the improvement concerns capacity constraints, non-differentiable cost functions and industry revenue functions that are discontinuous at 0.
Sufficient and necessary conditions for equilibrium uniqueness in aggregative games
Mouche, P.H.M. van; Yamazaki, T. - \ 2015
Journal of Nonlinear and Convex Analysis 16 (2015)2. - ISSN 1345-4773 - p. 353 - 364.
We identify sufficient and necessary conditions for an aggregative game to have a unique Nash equilibrium. In particular, an improvement of a result of Gaudet and Salant (1991) for Cournot oligopolies is obtained. The results are obtained by exploiting the general between Nash equilibria and fixed points of the (virtual) aggregate cumulative best reply correspondence.