Trembling Hand Research Articles

On perfect pairwise stable networks

We extend standard tools from equilibrium refinement theory in non-cooperative games to a cooperative framework of network formation. First, we introduce the new concept of perfect pairwise stability. It transposes the idea of “trembling hand” perfection to network formation theory and strictly refines the pairwise stability concept of Jackson and Wolinsky (1996). Second, we study basic properties of perfect pairwise stability: existence, admissibility and perturbation. We further show that our concept is distinct from the concept of strongly stable networks introduced by Jackson and Van den Nouweland (2005), and perfect Nash equilibria of the Myerson network formation game studied by Calvó-Armengol and İlkılıç (2009). Finally, we apply perfect pairwise stability to sequential network formation and prove that it enables a refinement of sequential pairwise stability, a natural analogue of subgame perfection in a setting with cooperative, pairwise link formation.

Twilight of Human Judgment

Twilight of Human Judgment

Paging Dr. Valentine: Racism and Allyship in Internship.

Paging Dr. Valentine: Racism and Allyship in Internship.

Detecting an Odd Restless Markov Arm With a Trembling Hand

In this paper, we consider a multi-armed bandit in which each arm is a Markov process evolving on a finite state space. The state space is common across the arms, and the arms are independent of each other. The transition probability matrix of one of the arms (the odd arm) is different from the common transition probability matrix of all the other arms. A decision maker, who knows these transition probability matrices, wishes to identify the odd arm as quickly as possible, while keeping the probability of decision error small. To do so, the decision maker collects observations from the arms by pulling the arms in a sequential manner, one at each discrete time instant. However, the decision maker has a trembling hand, and the arm that is actually pulled at any given time differs, with a small probability, from the one he intended to pull. The observation at any given time is the arm that is actually pulled and its current state. The Markov processes of the unobserved arms continue to evolve. This makes the arms restless. For the above setting, we derive the first known asymptotic lower bound on the expected time required to identify the odd arm, where the asymptotics is of vanishing error probability. The continued evolution of each arm adds a new dimension to the problem, leading to a family of Markov decision problems (MDPs) on a countable state space. We then stitch together certain parameterised solutions to these MDPs and obtain a sequence of strategies whose expected times to identify the odd arm come arbitrarily close to the lower bound in the regime of vanishing error probability. Prior works dealt with independent and identically distributed (across time) arms and rested Markov arms, whereas our work deals with restless Markov arms.

A note on the robustness of quantile treatment effect estimands

This note examines the robustness of two quantile treatment effect estimands to a perturbation away from the common effect assumption. The first estimand QY1−Y0(τ) is the τ-quantile of the difference between the potential outcomes and the second estimand QY1(τ)−QY0(τ) is the difference between the τ-quantiles of the potential outcomes. To this end, this note provides a simple “trembling hand” example whereby the treatment effect deviates from the common effect β for only one individual in a large population. As a result, each estimand deviates from β, and may have the opposite sign than β, in a distinct range of τ. In general, this perturbation leads QY1−Y0(⋅) to differ from β more severely but only in a small and extreme range of τ whereas it leads QY1(⋅)−QY0(⋅) to differ from β less severely but over a substantial and central range of τ. This example suggests that researchers should carefully evaluate estimates or bounds for QY1−Y0(τ) and especially QY1(τ)−QY0(τ) over a large range of τ.

Seeing my science clearly.

“You are about to witness a thesis implode,” I declared to my summer student. As I ran the critical sample through the flow cytometer, my trembling hand betrayed my nervousness that the result would confirm my worst fears: I had been fooling myself. Three years prior, I had been a bright-eyed first-year Ph.D. student. “This is guaranteed to give you data,” my mentor had said of the project he wanted me to take over. Preliminary data suggested that a poorly understood protein might trigger immune cells to kill cancer cells. It was an exciting possibility, but I was concerned. The previous rotation student had been unable to replicate the finding and wasn't convinced the protein did anything at all. But I couldn't turn down a project that sounded so promising. ![][1] ILLUSTRATION: ROBERT NEUBECKER > “I had been spinning a story … instead of critically examining the facts.” To my relief, a new batch of protein I prepared yielded striking results. The science unfurled into a thrilling jigsaw puzzle. Beautiful flow cytometry plots revealed that our protein induced immune cells to mature. In tissue culture experiments, these cells killed cancer cells with startling ferocity. The debut in vivo study showed that mice treated with the protein had only a fraction of the black melanoma spots we found in controls. I presented the results—collected on Christmas Eve, no less—at our weekly lab meeting with a mother's pride: A causes B causes C, in perfect alignment with our neatly constructed hypotheses. The results were so astounding, in fact, that they began to make me suspicious. I—along with my thesis committee members and adviser—wondered whether my results could be due to contamination from the bacterial system I used to produce the protein. After all, it seemed logical that a fragment of a pathogen, not our protein, could be what triggered the immune cells. However, I was soon reassured. I tested for contamination, looking for global immune activation, and everything looked clean. Relieved, I carried on. But about a year later, a reviewer for a grant application identified a flaw in the control I had put my trust in. It was a largely unknown quirk in immunology, heretofore untested because my committee members—like me and my adviser—saw the logical sense of the story I had synthesized. That is what led to the fateful moment at the flow cytometer, where I was testing a commercial sample of my protein certified to be free of any bacterial contaminants—a crucial control that I had previously been too blinded by preconceived expectations to devise. I was aghast when I saw that my protein in this pure state did nothing. My rotation student glanced at me, concerned. I chuckled darkly. I realized that I had been spinning a story from my science, interpreting my results based on my conception of what should be happening instead of critically examining the facts in front of me. I stepped away from the lab bench for a week and confronted my mistakes with brutal honesty that ended up being cathartic. My adviser did the same. I leaned on generous loved ones as I worked through what felt like the five stages of grief. At first, I lamented the loss of my tidy, compelling story, but I eventually realized that element of my grief was misplaced. As scientists, we seek to understand nature's crooked truth. To simplify it—as tempting as that can be—is contrary to our quest to do meaningful science. It took me 6 months to recover and find closure by taking on a new project. My adviser supported my new direction, and eventually I graduated with my Ph.D. I was burned, but the scars remind me to be a better scientist. Nowadays, I don't stop at controls. I really ponder my results. Could the cause be something other than what I expect? I am slower to draw easy conclusions and instead make sure to consider every possible variable. I have learned to detach myself from what I want my science to be, and instead allow the science to lead me to understanding what actually is. I listen to my doubts, no matter how much the puzzle fits and “makes sense” at first—or 20th—glance. [1]: /embed/graphic-1.gif

The Refined Best Reply Correspondence and Backward Induction

AbstractFixed points of the (most) refined best reply correspondence, introduced in Balkenborg et al. (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria are fixed points of this correspondence.

Iterative dominance in young children: Experimental evidence in simple two-person games

Abstract We investigate iterative reasoning in children from pre-kindergarten to first grade (4–7 years old). We consider two-person games that have a unique Trembling Hand Perfect Equilibrium but vary in three key features: iterative complexity (the number of iterations required to reach the equilibrium), perspective requirement (the identity of the player with whom the iteration should start) and action symmetry. The beliefs of participants regarding the decision of their partners are elicited either before or after their own choices are made. We obtain the following findings. (1) Iterative complexity is not necessarily a cause of equilibrium failure. (2) Games where the equilibrium action is the same for both players are correctly solved more often. (3) Starting a recursion by solving the problem of a different player is non-intuitive in all our age groups but it can be overcome by asking participants to think about their partner’s decision before making their own choices. (4) Such ex-ante belief elicitation can, however, be detrimental in complex asymmetric games. We discuss these results in the context of the development of logical abilities and theory of mind abilities.

Confidence of the trembling hand: Bayesian learning with data‐limited stocks

AbstractIn this paper, we argue that the static view of the Precautionary Principle that limits the risk of overfishing every season may be inconsistent with a dynamic perspective on precaution, where harvest control rules are adopted not only to limit fishing mortality every season, but also to infer extra information on the biological system through time. This additional information is capitalized into higher industry profits, via a reduction in the uncertainty faced by the regulator. Management of data‐poor fisheries typically relies on setting an annual catch limit (ACL) using catch‐based methods that are concerned with estimating a sustainable harvest and hinge on the logic that historic catches reflect a level of exploitation the stock can sustain. The resulting harvest control rules routinely set ACLs at the median (or mean) landings over a reference period, with or without a scalar downward adjustment according to the assumed level of depletion.Recommendations for Resource Managers: The prevalent use of catch‐based approaches to set ACLs in data‐limited fisheries, scalar methods, or variants that introduce dynamic updates according to estimates of depletion, may be suboptimal. It does not take into consideration the welfare benefits associated with the value of information acquired through alternative harvest control rules. We demonstrate that perturbations in the form of small, temporary, and intermittent increases to ACLs between stock assessments (combined with a safety valve), the “trembling‐hand,” can increase the permanent value of the stock. On the one hand, these perturbations translate into a more accurate estimation of the population model in the next assessment, which leads to ACLs closer to the true maximum sustainable yield thereafter. On the other hand, increases in ACLs imply a higher risk of overfishing. For a wide range of perturbations, the net present value (NPV) of industry profits under the trembling‐hand first‐order stochastically dominates that without perturbation.

SOFIA GUBAIDULINA’S RELATIONSHIP WITH GOD – COMPOSITIONAL, TECHNICAL AND INTERPRETATIONAL FEATURES OF HER MUSIC

The paper presents the compositions De Profundis for solo accordion, Et Exspecto for solo accordion and In Croce for accordion and cello, by one of the today’s highly appreciated composers, Sofia Gubaidulina. De Profundis is the first work by Gubaidulina for solo accordion, composed in 1978. In this work, Gubaidulina changed the ordinary sound of the accordion that she encountered in the Russian folk music, so that the sound of the accordion acquired a brand new dimension. Et Exspecto is the composition written in 1985 and has five movements. The composer expresses herself through different techniques and effects: air release valve, fast passages, tremolos, moving and static clusters, clusters by a trembling hand with a vibrato effect, etc. In Croce is a composition written in 1979 for cello and organ dedicated to the cellist Vladimir Tonkha. Gubaidulina, together with the accordion professor and artist Elsbeth Moser, rearranged In Croce for cello and accordion in 1991. The composition rests on specific crisscrossing of melodic lines, and it creates a visual impression of a cross with the listeners.

Tremors

As I am sure you can appreciate, my time spent here in the emergency room this afternoon has been unpleasant. During residency training, my emergency room rotation was the only one that required me to suture, something I avoided because as you often pointed out, I lack the hands of a surgeon. I chose to stitch up only the most inebriated patients, their drunken misadventures more scarring than poorly sewn lacerations. Ethanol is also a convenient anesthetic, and many times I probably could have done without even injecting lidocaine to freeze the skin. I still did, though, to practice guiding the needle with my trembling hand. To make up for my lack of dexterity, I spent hours each night poring over textbooks while you sat across from me, intently tying surgical knots. I would read aloud while you chimed in with this or that obscure fact, our duet set to the rhythm of your hands suturing the spliced skin of pigs' feet. In this way, we would study together. Yet I was perhaps only exceptional in how consistent my mediocrity was, and my clinical scores remained firmly average throughout our schooling. How you managed to effortlessly recall the minutiae of even our densest textbooks was beyond me, but I harbored no jealousy. On the contrary, I felt a sort of unjustified pride that I might play some small role in what was to become of you.

Information Theoretic Cutting of a Cake

Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e., one agent may like chocolate, while the other may like cream). A fair division of the cake is one that takes into account the individual valuations of agents and partitions of the cake based on some fairness criterion. Fair division may be accomplished in a distributed or centralized way. Due to its natural and practical appeal, it has been a subject of study in economics. To the best of our knowledge, the role of partial information in fair division has not been studied so far from an information theoretic perspective. Given the diversity of problems in fair division, we consider certain specific (yet important) problems that capture different aspects of information exchange in a fair division setting. From the class of distributed algorithms, we consider the classical divide and choose (DC) problem between two parties. Here, we study the effect of partial spying and voluntarily sharing of information in both one-shot and asymptotic scenarios. Furthermore, we consider implicit information transmission through actions for the repeated version of the problem. While identifying subgame perfect Nash equilibrium in repeated games with incomplete information on both sides is very difficult in general, for the special case of division of two items, we find a more stringent trembling hand perfect equilibrium. Next, from the class of centralized algorithms, we consider the Adjusted Winner (AW) algorithm between two players Alice and Bob. Brams and Taylor showed that if Alice can fully spy on Bob, she can trick the algorithm. We consider the same setup when partial spying is allowed and study the growth rate of Alice’s utility per spying bit. Via a transformation from AW to DC, it is shown that the problem reduces to the one studied earlier for DC. However, if Alice is forced to only spy certain simple structured functions of Bob’s valuation, an upper bound on the growth rate of utility per spying bit is derived. This bound is shown to be tight in some cases. We also consider a centralized algorithm for maximizing the overall welfare of the agents under the Nash collective utility function (CUF). This corresponds to a clustering problem. By observing a link between this problem and the portfolio selection problem in stock markets, we provide an upper bound on the increase of the Nash CUF for a clustering refinement.

Symmetric Equilibria in a Cost-Averting War of Attrition Requiring Minimum Necessary Conceders

AbstractThis paper provides an analysis of a cost-averting war of attrition with minimum necessary conceders. All symmetric stationary Nash equilibria are characterized. The multiplicity of equilibria has called for further refinements. We show that there exists a unique symmetric stationary trembling hand perfect equilibrium. Comparative statics results of the trembling hand perfect equilibrium are provided. This paper’s model is motivated by the problem of delayed public goods provisions in collective action settings. Augmenting the number of minimum necessary conceders can curtail delays.

Supporting Trembling Hand Typing Using Optical See-Through Mixed Reality

A tremor is an involuntary rhythmic shaking movement of the muscles, which reduces the precision of hand and finger movements. It is difficult for individuals with hand tremors to type accurately using small- and high-density targets, such as keyboard. This research proposes an optical see-through mixed reality system that reduces hand tremors so that the individual can type steadily. The system virtually stabilizes the individual’s hand tremors by optically overlapping the trembling hand with a stabilized virtual hand to produce a realistic typing sensation without any tremors. The simulation experiments proved that the system supports trembling hand typing. By comprehensively investigating both the objective (time and error ratios) and the subjective (the sense of ownership, agency, and pertinence) aspects, the system with a virtual:real intensity ratio of 0.75:0.25 was found to be optimal.

Behavior and Biased Choice: A Pitcher’s Problem

A game-theoretic model can not incorporate behavioral attitudes. For more effective prediction, the model can be augmented with the reflection of irrational choices. Pitcher’s problem of baseball can be a useful example to show association between strategic choice and behavioral attitude. On mound, the pitcher should encounter great risk of possible unwanted outcome. Confronting the risk, he might be inclined to choose the comfortable strategy, which can reduce possibility of trembling hand. The pitcher’s decision can be explained in two-dimensions: rationality and irrationality. In this paper, we will consider a situation that mixed strategy can be chosen. Intuitively, behavioral attitude is believed to generate some bias on probability distribution assigned for the strategies. That is, likeliness of choosing one pure strategy can be biased depending on behavioral attitude of the individual. Understanding the individuality of the player can contribute to anticipating how he would make a choice.

How Risky is it to Deviate from Nash Equilibrium?

The purpose of this work is to offer for each player and any Nash equilibrium (NE), a measure for the potential risk in deviating from the NE strategy in any two person matrix game. We present two approaches regarding the nature of deviations: Strategic and Accidental. Accordingly, we define two models: S-model and T-model. The S-model defines a new game in which players deviate in the least dangerous direction. The risk defined in the T-model can serve as a refinement for the notion of “trembling hand perfect equilibrium” introduced by R. Selten. The risk measures enable testing and evaluating predictions on the behavior of players. For example: do players deviate more from a NE that is less risky? This may be relevant to the design of experiments. We present an Integer programming problem that computes the risk for any given player and NE. In the special case of zero-sum games with a unique strictly mixed NE, we prove that the risks of the players always coincide, even if the game is far from symmetry. This result holds for any norm we use for the size of deviations. We compare our risk measures to the risk measure defined by Harsanyi and Selten which is based on criteria of stability rather than on potential damage. We show that the measures may contradict.

Strategic customer behavior facing possible stockout: An experimental study

This paper studies strategic customer behavior in a monopolistic seller system. Given the stock quantity and the selling prices, a customer chooses either to buy at the full price to certainly obtain a product or to wait for a discount with the risk of stockout. We model the behavior of strategic customers as a customer-game. It is shown that the customer-game may have multiple Nash equilibria. Specifically, in the condition of weak incentive compatibility, the trembling hand perfect equilibrium is “all-wait”, which is inconsistent with the “all-buy” assumption in the literature. We conduct laboratory experiments to investigate behavior of strategic customers. The results show that customers' behaviors exhibit a deviation from Nash equilibria. Using a framework of quantal response equilibrium, we develop behavioral models to effectively characterize the behavior of strategic customers.

Compliance signaling games: toward modeling the deterrence of insider threats

In a typical workplace, organizational policies and their compliance requirements set the stage upon which the behavioral patterns of individual agents evolve. The agents' personal utilities, access to information, and strategic deceptions shape the signaling systems of an intricate information-asymmetric game, thus mystifying assessment and management of organizational risks, which are primarily due to unintentional insider threats. Compliance games, as discussed here, model a rudimentary version of this signaling game between a sender (employee) and a receiver (organization). The analysis of these games' equilibria as well as their dynamics in repeated game settings illuminate the effectiveness or risks of an organizational policy. These questions are explored via a repeated and agent-based simulation of compliance signaling games, leading to the following: (1) a simple but broadly applicable model for interactions between sender agents (employees) and receiver agents (principals in the organization), (2) an investigation of how the game theoretic approach yields the plausible dynamics of compliance, and (3) design of experiments to estimate parameters of the systems: evolutionary learning rates of agents, the efficacy of auditing using a trembling hand strategy, effects of non-stationary and multiple principal agents, and ultimately, the robustness of the system under perturbation of various related parameters (costs, penalties, benefits, etc.). The paper concludes with a number of empirical studies, illustrating a battery of compliance games under varying environments designed to investigate agent based learning, system control, and optimization. The studies indicate how agents through limited interactions described by behavior traces may learn and optimize responses to a stationary defense, expose sensitive parameters and emergent properties and indicate the possibility of controlling interventions which actuate game parameters. We believe that the work is of practical importance--for example, in constraining the vulnerability surfaces arising from compliance games.

Science visualized: Diagnosing what caused a medieval trembling hand

Science visualized: Diagnosing what caused a medieval trembling hand

To punish or to leave: distinct cognitive processes underlie partner control and partner choice behaviors.

When a cooperative partner defects, at least two types of response are available: Punishment, aimed at modifying behavior, and ostracism, aimed at avoiding further social interaction with the partner. These options, termed partner control and partner choice, have been distinguished at behavioral and evolutionary levels. However, little work has compared their cognitive bases. Do these disparate behaviors depend on common processes of moral evaluation? Specifically, we assess whether they show identical patterns of dependence on two key dimensions of moral evaluation: A person’s intentions, and the outcomes that they cause. We address this issue in a “trembling hand” economic game. In this game, an allocator divides a monetary stake between themselves and a responder based on a stochastic mechanism. This allows for dissociations between the allocator’s intent and the actual outcome. Responders were either given the opportunity to punish or reward the allocator (partner control) or to switch to a different partner for a subsequent round of play (partner choice). Our results suggest that partner control and partner choice behaviors are supported by distinct underlying cognitive processes: Partner control exhibits greater sensitivity to the outcomes a partner causes, while partner choice is influenced almost exclusively by a partner’s intentions. This cognitive dissociation can be understood in light of the unique adaptive functions of partner control and partner choice.