Page 553 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 553
A GAME THEORY AND ITS APPLICATIONS (MS-56)
Schumpeterian Evolution of Consumers’ Optima – A Game Theory
Insight
Marta Kornafel, marta.kornafel@uek.krakow.pl
Cracow University of Economics, Poland
We will consider the behaviour of consumers’ optimal allocations in the result of Schumpeter
evolution of economy. The goal of consumer in general equilibrium model is to choose an
optimal allocation that maximises his preferences over the budget set, given the price and initial
allocation. The crucial point is to justify – taking into account the changing preferences – that
the consumers choosing the optimal allocation at every stage of evolutionary process will end
up at an optimal state of the final economy. In the talk we will provide the conditions, under
which the positive answer is possible.
Nash Equilibria in certain two-choice multi-player games played on the
ladder graph
Victoria Sánchez Muñoz, v.sanchezmunoz1@nuigalway.ie
National University of Ireland Galway, Ireland
Coauthor: Michael Mc Gettrick
We compute analytically the number of Nash Equilibria (NE) for a two-choice game played
on a (circular) ladder graph with 2n players. We consider a set of games with generic payoff
parameters, with the only requirement that a NE occurs if the players choose opposite strategies
(anti-coordination game). The results show that for both, the ladder and circular ladder, the
number of NE grows exponentially with (half) the number of players n, as NNE(2n) ∼ C(ϕ)n,
where ϕ = 1.618... is the golden ratio and Ccirc > Cladder. In addition, the value of the scaling
factor Cladder depends on the value of the payoff parameters. However, that is no longer true
for the circular ladder (3-degree graph), that is Ccirc is constant, which might suggest that the
topology of the graph indeed plays an important role for setting the number of NE.
Expected duration in multilateral selection problems
Krzysztof Szajowski, krzysztof.szajowski@pwr.edu.pl
Wroclaw University of Science and Technology, Poland
This paper treats the decision problem related to the observation of a Markov process by de-
cision makers. The information delivered to the players is based on the aggregation of the
high-frequency data by some functions. Admissible strategies are stopping moments related
to the available information. The payments are defined by the state at the time of stopping.
The players’ decision to stop has various effects which depend on the decision makers’ type
(v. [3]). The knowledge about the type of the players is not public and in this way, the payers
have also different information. The details of the description allow to formulate the problem
as a Bayesian game with sets of strategies based on the stopping times. It is an extension of
the Dynkin’s game related to the observation of a Markov process with the random assignment
mechanism of states to the players. The main question considered now is the expected duration
of each DM in the game (v. [1]). Some examples related to the best choice problem (BCP) are
551
Schumpeterian Evolution of Consumers’ Optima – A Game Theory
Insight
Marta Kornafel, marta.kornafel@uek.krakow.pl
Cracow University of Economics, Poland
We will consider the behaviour of consumers’ optimal allocations in the result of Schumpeter
evolution of economy. The goal of consumer in general equilibrium model is to choose an
optimal allocation that maximises his preferences over the budget set, given the price and initial
allocation. The crucial point is to justify – taking into account the changing preferences – that
the consumers choosing the optimal allocation at every stage of evolutionary process will end
up at an optimal state of the final economy. In the talk we will provide the conditions, under
which the positive answer is possible.
Nash Equilibria in certain two-choice multi-player games played on the
ladder graph
Victoria Sánchez Muñoz, v.sanchezmunoz1@nuigalway.ie
National University of Ireland Galway, Ireland
Coauthor: Michael Mc Gettrick
We compute analytically the number of Nash Equilibria (NE) for a two-choice game played
on a (circular) ladder graph with 2n players. We consider a set of games with generic payoff
parameters, with the only requirement that a NE occurs if the players choose opposite strategies
(anti-coordination game). The results show that for both, the ladder and circular ladder, the
number of NE grows exponentially with (half) the number of players n, as NNE(2n) ∼ C(ϕ)n,
where ϕ = 1.618... is the golden ratio and Ccirc > Cladder. In addition, the value of the scaling
factor Cladder depends on the value of the payoff parameters. However, that is no longer true
for the circular ladder (3-degree graph), that is Ccirc is constant, which might suggest that the
topology of the graph indeed plays an important role for setting the number of NE.
Expected duration in multilateral selection problems
Krzysztof Szajowski, krzysztof.szajowski@pwr.edu.pl
Wroclaw University of Science and Technology, Poland
This paper treats the decision problem related to the observation of a Markov process by de-
cision makers. The information delivered to the players is based on the aggregation of the
high-frequency data by some functions. Admissible strategies are stopping moments related
to the available information. The payments are defined by the state at the time of stopping.
The players’ decision to stop has various effects which depend on the decision makers’ type
(v. [3]). The knowledge about the type of the players is not public and in this way, the payers
have also different information. The details of the description allow to formulate the problem
as a Bayesian game with sets of strategies based on the stopping times. It is an extension of
the Dynkin’s game related to the observation of a Markov process with the random assignment
mechanism of states to the players. The main question considered now is the expected duration
of each DM in the game (v. [1]). Some examples related to the best choice problem (BCP) are
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