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Constrained and indefinite games and their applications

100%
Wieczorek A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction................................5    Preliminaries...........................6 I. Games....................................9    1. Constrained games............9    2. Indefinite games...............13 II. Applications.........................18    3. Model A: atomless............18    4. Model B: atomic................26 Appendix..................................30 References..............................40 Subject index...........................42
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Large games with only small players and strategy sets in Euclidean spaces

96%
Wieczorek A.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 2
183-193
EN
The games of type considered in the present paper (LSE-games) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence of equilibria and present a minimization problem and a complementarity problem (both nonlinear) whose solutions are exactly the same as equilibria in the given game. Examples of applications include a model of social adaptation and a model of economic efficiency enforced by taxation.
3
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Large games with only small players and finite strategy sets

96%
Wieczorek A.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 1
79-96
EN
Large games of kind considered in the present paper (LSF-games) directly generalize the usual concept of n-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity and constrained optimization procedures in Euclidean spaces. The games are shown to fit well the voting procedures and evolutionary processes. As an example of application, we present a model of production and consumption by infinitely many households; a competitive equilibrium is obtained via a reduction to an LSF-game; the equilibrating market mechanism is modelled by actions of infinitely many small corrective powers.
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On a multi-objective optimization problem arising from production theory

61%
Roman M., Wieczorek A.
Applicationes Mathematicae
|
1998-1999
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tom 25
|
nr 4
411-415
EN
The paper presents a natural application of multi-objective programming to household production and consumption theory. A contribution to multi-objective programming theory is also included.
5
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Core solutions and nash equilibria in noncooperative games with a measure space of players

61%
Flåm S., Wieczorek A.
Banach Center Publications
|
2006
|
tom 71
|
nr 1
115-123
EN
The paper deals with noncooperative games in which players constitute a measure space. Strategy profiles that are equal almost everywhere are assumed to have the same interactive effects. Under these circumstances we explore links between core solutions and Nash equilibria. Conditions are given which guarantee that core outcomes must be Nash equilibria and vice versa. The main contribution are results on nonemptieness of the core.
6
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Ordering probabilities on an ordered measurable space

36%
Wieczorek A.
Fundamenta Mathematicae
|
1978
|
tom 101
|
nr 1
53-78
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