A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

Three essays on game theory and bargaining

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Bargaining over strategies of non-cooperative games

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.

Nash equilibria in multi-agent motor interactions.

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.

Non-existence of competitive equilibria with dynamically inconsistent preferences

This paper shows the robust non-existence of competitive equilibria even in a simple three period representative agent economy with dynamically inconsistent preferences. We distinguish between a sophisticated and naive representative agent. Even when underlying preferences are monotone and convex, at given prices, we show by example that the induced preference of the sophisticated representative agent over choices in first-period markets is both non-convex and satiated. Even allowing for negative prices, the market-clearing allocation is not contained in the convex hull of demand. Finally, with a naive representative agent, we show that perfect foresight is incompatible with market clearing and individual optimization at given prices.

Bertrand, Cournot and monopolistically competitive equilibria

Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.

Word-perfect Gatsby overcomes its flaws

Review of 'Gatz', Elevator Repair Company / Brisbane Powerhouse, published in The Australian, 12 May 2009.

Towards a provably secure DoS-Resilient key exchange protocol with perfect forward secrecy

Just Fast Keying (JFK) is a simple, efficient and secure key exchange protocol proposed by Aiello et al. (ACM TISSEC, 2004). JFK is well known for its novel design features, notably its resistance to denial-of-service (DoS) attacks. Using Meadows’ cost-based framework, we identify a new DoS vulnerability in JFK. The JFK protocol is claimed secure in the Canetti-Krawczyk model under the Decisional Diffie-Hellman (DDH) assumption. We show that security of the JFK protocol, when reusing ephemeral Diffie-Hellman keys, appears to require the Gap Diffie-Hellman (GDH) assumption in the random oracle model. We propose a new variant of JFK that avoids the identified DoS vulnerability and provides perfect forward secrecy even under the DDH assumption, achieving the full security promised by the JFK protocol.

The cost of being perfect : perfectionism and suicide ideation in university students

Objective: The aim of the study was to assess the relationship between dimensions of perfectionism and suicide ideation in a tertiary student population in Australia. Method: The methodology involved 405 students completing the General Health Questionnaire (GHQ-28) which includes a subset of questions which can be used to assess suicide ideation, and the Multidimensional Perfectionism Scale. Results: The presence of suicide ideation was associated with higher scores on total perfectionism and two perfectionism dimensions, and total GHQ scores. There were significant differences between participants with high levels of perfectionism and participants with moderate to low levels of perfectionism on a measure of suicide ideation. Neither gender nor age were associated with differences in the scores, with results indicating high levels of perfectionism may indicate a vulnerability to suicide ideation. Conclusions: Perfectionism is a valued attribute in high-achieving populations. The question needs to be asked, however, at what cost? The findings indicate that high levels of perfectionism may be associated with an increased vulnerability to suicide ideation. Future research is needed to gain a better understanding of the complex interrelationship between personality and temperament, environmental factors and self-destructive behaviour.

Forrest v ASIC : a ‘perfect storm’

The policy objectives of the continuous disclosure regime augmented by the misleading or deceptive conduct provisions in the Corporations Act are to enhance the integrity and efficiency of Australian capital markets by ensuring equality of opportunity for all investors through public access to accurate and material company information to enable them to make well-informed investment decisions. This article argues that there were failures by the regulators in the performance of their roles to protect the interests of investors in Forrest v ASIC; FMG v ASIC (2012) 247 CLR 486: ASX failed to enforce timely compliance with the continuous disclosure regime and ensure that the market was properly informed by seeking immediate clarification from FMG as to the agreed fixed price and/or seeking production of a copy of the CREC agreement; and ASIC failed to succeed in the High Court because of the way it pleaded its case. The article also examines the reasoning of the High Court in Forrest v ASIC and whether it might have changed previous understandings of the Campomar test for determining whether representations directed to the public generally are misleading.

Baidu’s perfect paradox : free speech and the right to censor

China’s biggest search engine has a constitutional right to filter its search results, a US court found last month. But that’s just the start of the story. Eight New York-based pro-democracy activists sued Baidu Inc in 2011, seeking damages because Baidu prevents their work from showing up in search results. Baidu follows Chinese law that requires it to censor politically sensitive results. But in what the plaintiffs’ lawyer has dubbed a “perfect paradox”, US District Judge Jesse Furman has dismissed the challenge, explaining that to hold Baidu liable for its decisions to censor pro-democracy content would itself infringe the right to free speech.