Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets—Phase Transition

Campbell, Michael J.; Carfì, David

doi:10.1007/s10955-017-1915-7

Cited by 9 publications

(9 citation statements)

References 52 publications

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“…This independence of the index i when matching first derivatives of the potential and actions is an alternate way to demonstrate the condition in (11) as manifested in (12) for the quadratic case.…”

Section: Potential Gamesmentioning

confidence: 89%

“…Quadratic models originate as far back as 1838 in a Cournot competition with linear price [5]. More recently, variations on a Cournot competition with localized demand were studied in [6], and a quadratic game-theoretic model of financial interactions among a hedging agent and speculators was examined in [7,8,9,10,11]. The work [12] contains various applications of quadratic models: crime, education, industrial organization, cities, conformity and conspicuous effects.…”

Section: History Of the Modelmentioning

confidence: 99%

“…Without loss of generality, assume i < j. The conditions in (11) imply that the coefficients in (9) satisfy…”

Section: Potential Gamesmentioning

confidence: 99%

“…Example 4 (Quantity/Price-Payoff Model of Action Functions). The linear-demand Cournot model [5] as well as a two-market model of financial markets with speculators and hedgers [8,9,10,11,7] have payoff functions of the form…”

Section: Potential Gamesmentioning

confidence: 99%

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An elementary humanomics approach to boundedly rational quadratic models

Campbell

Smith

2021

Physica A: Statistical Mechanics and its Applications

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We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resentment evolution ("annealed" model) is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A twoagent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1 − p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p * i , i = 1, 2, exists for each agent. When p < p * i , agent i will choose action in their self-interest. When p > p * i , agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p * i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.

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Section: Potential Gamesmentioning

confidence: 89%

Section: History Of the Modelmentioning

confidence: 99%

“…Without loss of generality, assume i < j. The conditions in (11) imply that the coefficients in (9) satisfy…”

Section: Potential Gamesmentioning

confidence: 99%

Section: Potential Gamesmentioning

confidence: 99%

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An elementary humanomics approach to boundedly rational quadratic models

Campbell

Smith

2021

Physica A: Statistical Mechanics and its Applications

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“…As concerns the complete analysis of classic duopoly model, see [9,10]. Other applications of game theory to economic duopolies can be found in [11][12][13][14][15][16][17][18]. For a Radon and Schwartz distribution approach to probability, see [19][20][21].…”

Section: Bayesian Games In Industrial Organizationmentioning

confidence: 99%

Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Carfì

Donato

2018

Mathematics

Self Cite

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In this paper, we consider a Cournot duopoly, in which any firm does not know the marginal costs of production of the other player, as a Bayesian game. In our game, the marginal costs depend on two infinite continuous sets of states of the world. We shall study, before the general case, an intermediate case in which only one player, the second one, shows infinitely many types. Then, we shall generalize to the case in which both players show infinitely many types depending on the marginal costs, where the marginal costs are given by the nature and each actual marginal cost is known only by the respective player. We find, in both cases, the general Nash equilibrium.

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