Uncertain Information Structures and Backward Induction

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents'capacity to acquire,interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational,(ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and op-ponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends {from generic games with perfect information to games with not necessarily perfect information{the work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.

Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)

We define Nash equilibrium for two-person normal form games in the presence of uncertainty, in the sense of Knight(1921). We use the fonna1iution of uncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibria for any degree of uncertainty, as measured by the uncertainty aversion (Dow anel Wer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationaliuble in the usual sense. Next, we break down backward industion in the twice repeated prisoner's dilemma. We link these results with those on cooperation in the finitely repeated prisoner's dilemma obtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this mode1 of equilibrium does not display logical omniscience.

Nash equilibrium under knightian uncertainty: breaking-down backward induction

We present two alternative definitions of Nash equilibrium for two person games in the presence af uncertainty, in the sense of Knight. We use the formalization of uncertainty due to Schmeidler and Gilboa. We show that, with one of the definitions, prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationalizable in the usual sense. Most striking is that with the Same definition we break down backward induction in the twice repeated prisoner's dilemma. We also link these results with the Kreps-Milgrom-Roberts-Wilson explanation of cooperation in the finitely repeated prisoner's dilemma.

Decision-theoretic designs for dose-finding clinical trials with multiple outcomes

A decision-theoretic framework is proposed for designing sequential dose-finding trials with multiple outcomes. The optimal strategy is solvable theoretically via backward induction. However, for dose-finding studies involving k doses, the computational complexity is the same as the bandit problem with k-dependent arms, which is computationally prohibitive. We therefore provide two computationally compromised strategies, which is of practical interest as the computational complexity is greatly reduced: one is closely related to the continual reassessment method (CRM), and the other improves CRM and approximates to the optimal strategy better. In particular, we present the framework for phase I/II trials with multiple outcomes. Applications to a pediatric HIV trial and a cancer chemotherapy trial are given to illustrate the proposed approach. Simulation results for the two trials show that the computationally compromised strategy can perform well and appear to be ethical for allocating patients. The proposed framework can provide better approximation to the optimal strategy if more extensive computing is available.

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 .

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Three essays on labor liberalization and its effects on world economy

This dissertation consists of three theoretical essays on immigration, international trade and political economy. The first two essays analyze the political economy of immigration in developed countries. The third essay explores new ground on the effects of labor liberalization in developing countries. Trade economists have witnessed remarkable methodological developments in mathematical and game theoretical models during the last seventy years. This dissertation benefits from these advances to analyze economic issues related to immigration. The first essay applies a long run general equilibrium trade model similar to Krugman (1980), and blends it with the median voter ala-Mayer (1984) framework. The second essay uses a short run general equilibrium specific factor trade model similar to Jones (1975) and incorporates it with the median voter model similar to Benhabib (1997). The third essay employs a five stage game theoretical approach similar to Vogel (2007) and solves it by the method of backward induction. The first essay shows that labor liberalization is more likely to come about in societies that have more taste for varieties, and that workers and capital owners could share the same positive stance toward labor liberalization. In a dynamic model, it demonstrates that the median voter is willing to accept fewer immigrants in the first period in order to preserve her domestic political influence in the second period threatened by the naturalization of these immigrants. The second essay shows that the liberalization of labor depends on the host country's stock and distribution of capital, and the number of groups of skilled workers within each country. I demonstrate that the more types of goods both countries produce, the more liberal the host country is toward immigration. The third essay proposes a theory of free movement of goods and labor between two economies with imperfect labor contracts. The heart of my analysis lies in the determinants of talent development where individuals' decisions to emigrate are related to the fixed costs of emigration. Finally, free trade and labor affect income via an indirect effect on individuals' incentives to invest in the skill levels and a direct effect on the prices of goods.

Contribution du mécanisme d'inhibition présynaptique à l'induction de réactions posturales efficaces suite à une perturbation d'équilibre

Le risque de chute est une problématique bien présente chez les personnes âgées ou ayant une atteinte neurologique et reflète un déficit des mécanismes neuronaux assurant l’équilibre. De précédentes études démontrent que l’intégration des informations sensorielles est essentielle au contrôle de l’équilibre et que l’inhibition présynaptique (IP) serait un mécanisme important dans le contrôle de la transmission sensorielle. Ainsi, le but de cette étude était d’identifier la contribution du mécanisme d’IP à l’induction de réponses posturales efficaces suite à une perturbation d’équilibre. Notre hypothèse est qu’une diminution d’IP contribuerait à l’induction des ces réponses, en augmentant l’influence de la rétroaction sensorielle sur les réseaux de neurones spinaux. Afin de démontrer cette hypothèse, nous avons d’abord évalué l’excitabilité spinale pendant les perturbations vers l’avant ou vers l’arrière, à l’aide du réflexe H. L’excitabilité spinale était modulée selon la direction de la perturbation et cette modulation survenait dès 75 ou 100 ms (p<0.05), soit avant l’induction des réactions posturales. Puis, à l’aide de techniques plus précises de convergence spinale, nous avons démontré que l’IP était diminuée dès 75 et 100 ms dans les deux directions, suggérant que la transmission des informations sensorielles vers la moelle épinière est accrue juste avant le déclenchement de la réponse posturale. Cette étude met en évidence un mécanisme-clé permettant d’augmenter la rétroaction des informations sensorielles nécessaires à l’induction de réponses posturales appropriées. L’évaluation de ce mécanisme pourrait mener à une meilleure identification des individus à risque de chute.

Teacher induction in Australia : a sample of what’s really happening

Retention rates and stress levels of beginning teachers are of concern. Well-planned induction programs can assist beginning teachers to make the transition successfully into the profession, which may increase retention rates. This qualitative, year-long study aims to explore and describe the induction experiences of eight beginning teachers as they negotiated their first year of teaching. Data gathered through interviews and emails indicated that these teachers required further development on: catering for individual differences, assessing in terms of outcomes, relating to parents, relating to the wider community, and understanding school policies; however, relating to students and understanding legal responsibilities and duty of care were not issues. At the conclusion of their first year only one beginning teacher was assisted by a mentor (veteran teacher) on whole-school programming, and planning for improving teaching with opportunities to visit other classrooms. This was also the only beginning teacher who received a reduced workload in order to meet with the mentor to discuss pedagogical developments. The inadequate support provided to beginning teachers in this study highlights the need for principals and school staff to reassess induction processes, which includes providing time, funding, mentoring support and clear guidelines for a quality induction program.

A forward and backward secure key management in wireless sensor networks for PCS/SCADA

Process Control Systems (PCSs) or Supervisory Control and Data Acquisition (SCADA) systems have recently been added to the already wide collection of wireless sensor networks applications. The PCS/SCADA environment is somewhat more amenable to the use of heavy cryptographic mechanisms such as public key cryptography than other sensor application environments. The sensor nodes in the environment, however, are still open to devastating attacks such as node capture, which makes designing a secure key management challenging. In this paper, a key management scheme is proposed to defeat node capture attack by offering both forward and backward secrecies. Our scheme overcomes the pitfalls which Nilsson et al.'s scheme suffers from, and is not more expensive than their scheme.

Investigation of shaft voltage in wind turbine systems with induction generators

This paper presents the analysis of shaft voltage in different configurations of a doubly fed induction generator (DFIG) and an induction generator (IG) with a back-to-back inverter in wind turbine applications. Detailed high frequency model of the proposed systems have been developed based on existing capacitive couplings in IG & DFIG structures and common mode voltage sources. In this research work, several arrangements of DFIG based wind energy conversion systems (WES) are investigated in case of shaft voltage calculation and its mitigation techniques. Placements of an LC line filter in different locations and its effects on shaft voltage elimination are studied via Mathematical analysis and simulations. A pulse width modulation (PWM) technique and a back-to-back inverter with a bidirectional buck converter have been presented to eliminate the shaft voltage in a DFIG wind turbine.

Calculations of capacitive couplings in induction generators to analyse shaft voltage

This paper deals with the analysis of the parameters which are effective in shaft voltage generation of induction generators. It focuses on different parasitic capacitive couplings by mathematical equations, finite element simulations and experiments. The effects of different design parameters have been studied on proposed capacitances and resultant shaft voltage. Some parameters can change proposed capacitive coupling such as: stator slot tooth, the gap between slot tooth and winding, and the height of the slot tooth, as well as the air gap between the rotor and the stator. This analysis can be used in a primary stage of a generator design to reduce motor shaft voltage and avoid additional costs of resultant bearing current mitigation.