Lower Payoffs Research Articles

Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems

The aim of this paper is to examine some American-style financial instruments that lead to two-sided optimal hitting problems. We pay particular attention to derivatives that are similar to strangle options but have a quadratic payoff function. We consider these derivatives in light of much more general payoff structures under certain conditions which guarantee that the optimal strategy is an exit from a strip. Closed-form formulas for the optimal boundaries and the fair price are derived when the contract has no maturity constraints. We obtain the form of the optimal boundaries under the finite maturity horizon and approximate them by maximizing the financial utility of the derivative holder. The Crank–Nicolson finite difference method is applied to the pricing problem. The importance of these novel financial instruments is supported by several features that are very useful for financial practice. They combine the characteristics of the power options and the ordinary American straddles. Quadratic strangles are suitable for investors who need to hedge strongly, far from the strike positions. In contrast, the near-the-money positions offer a relatively lower payoff than the ordinary straddles. Note that the usual options pay exactly the overprice; no more, no less. In addition, the quadratic strangles allow investors to hedge the positions below and above the strike together. This is very useful in periods of high volatility when large market movements are expected but their direction is unknown.

Navigating bias? An assessment of access to, use of, and returns to social capital in the school-to-work transition of descendants of immigrants

Research in several advanced economies has found that the descendants of immigrants tend to experience persistent difficulties in entering the labour market. This article tests whether social capital contributes to the disadvantage of descendants of immigrants in the school-to-work transition when compared to their native-background peers in Sweden. The study uses the CILS4EU survey, which provides information on friendship ties measured at age 15 and labour market outcomes at age 19. This allows for an analysis of networks formed before labour market entrance, an extensive control setup, and a comparison of measures of outgoing, incoming, and reciprocated friendship ties. The results show that the descendants of immigrants have access to less social capital measured as employed friends, but that they are as likely as natives to use their contacts to obtain a job. The returns to social capital are similar in terms of unemployment risk, but descendants of immigrants have a lower payoff when it comes to earnings. The study concludes that social capital contributes to, but is not the main driver of their labour market disadvantage in the school-to-work transition.

To Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-Player Trust Game

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g. to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g. not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g. to trust). A generalisation of the TG to a multiplayer (i.e. more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles; instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players.

The spatial public goods game on hypergraphs with heterogeneous investment

The emergence of cooperation in the multi-person social dilemma has been extensive investigated under the pairwise interactions-based spatial public goods game (PGG). However, higher-order interactions are more suitable to describe the group relationships in real society and have attracted intensive interests. In this work, we propose an extension of the spatial PGG on hypergraphs, where cooperators are allowed to allocate their investments unevenly. A tunable parameter, α, is introduced to characterize the investment preference. α>0 means that cooperators will allocate more investment to the PGG group from which they obtain higher payoff, while for α<0, cooperators will allocate more investment to the group from which they gain lower payoff. Results from numerical simulations indicate that compared with the results of homogeneous case, allocating more resources to profitable groups can effectively promote cooperation. Additionally, for a relative high synergy factor r, there exists a moderate negative value of α that will induce the lowest cooperation level, larger or smaller values of α can enable a higher cooperation level relative to the worst result. Moreover, the nontrivial results are robust against hypergraphs with different orders.

Collusion and predation under Cournot competition

This paper studies how predation strategies can affect the sustainability of collusion in a duopoly. Collusion may be sustained at equilibrium for intermediate discount factors. In such instances, predation implies that punishment strategies will yield low subgame perfect payoffs, thereby making collusion easier to sustain. For low discount factors, collusion is not sustainable because of the high incentives to deviate to Cournot–Nash strategies. Moreover, for high discount factors, it is always optimal to predate a colluding firm, thus contrasting with much of the earlier literature showing that collusion is only achievable by sufficiently patient firms.

Sampling dynamics applied to the traveler's dilemma reveals non-Nash behavior

The traveler's dilemma is characterized by a strict Nash equilibrium that is Pareto-inefficient. Even though a coordinated choice of more efficient options would be preferred by both players, any individual deviation from Nash behavior will induce a lower payoff. Yet experimental behavior reported in the literature demonstrates that deviations from Nash behavior toward Pareto-better outcomes are typical. An application of the sampling dynamics to this dilemma further justifies the non-Nash behavior. Due to the fact, that the sampling dynamics is not payoff-monotonic, even dominated strategies can survive the selection process. It is shown that for a generalized traveler's dilemma an interior equilibrium attracts almost all trajectories, given that there are sufficiently many options. The limit for infinitely many options is derived.

Bargaining over Treatment Choice under Disagreement

A group of experts with different prior beliefs must choose a treatment. A dataset is made public and leads to revisions of beliefs. We propose a model where the experts’ disagreements are resolved through bargaining, using the Nash bargaining solution. Experts bargain after disclosure of the dataset. Bargaining may lead to an inefficient use of information in a strong sense: experts receive a lower payoff in every state and for any prior belief (i.e., inadmissibility). Bargaining exhibits underreaction to information as compared to the normative solution in which experts bargain ex ante on the procedure used to exploit the data. (JEL C78, D82, D83)

Unexpected paths to cooperation on tied hyperbolic networks

Hyperbolic networks have high clustering, short average path lengths, and community structure, which are all properties that are commonly associated with social networks. As such, these networks constitute the perfect playing ground for probing factors that may affect public cooperation in realistic scenarios. And although much is already known about the evolution of cooperation on networks, we here consider the public goods game on tied hyperbolic networks, such that payoffs in one network layer influence the payoffs in the other and vice versa. We also consider random, assortative, and disassortative mixing in the networks to account for varying connections between players over time. While our research confirms the overall positive impact of interdependent payoffs, we also find that mixing on the network where cooperation thrives may strongly promote the cooperation in the other network, while destroying it completely in the former. We show that this is related to the mapping of lower payoffs from one network to the other, where cooperators in one network benefit from the failure of cooperators in the other network. Namely, as soon as the multiplication factor for the public goods is high enough to nullify the negative effects of mixing and cooperators thus recover, the positive effect on cooperation in the other network vanishes. We determine optimal conditions for this phenomenon in terms of the frequency of mixing and the strength of ties between the payoffs on both networks, and we discuss the implications of our research for enhanced cooperation in coupled populations, in particular in the light of mutual success not always being desirable for cooperation to thrive.

Dynamic Privacy Choices

I study a dynamic model of consumer privacy and platform data collection. In each period consumers choose their level of platform activity. Greater activity generates more information about the consumer, thereby increasing platform profits. When the platform can commit to the future privacy policy, it collects information by committing to gradually decreasing the level of privacy protection. In the long run consumers lose privacy and receive low payoffs but choose high activity levels. In contrast, the platform with weaker commitment power may attain the commitment outcome or fail to collect any data depending on consumer expectations regarding future privacy protection. (JEL C93, D11, D82, D83, D84, L86)

Which misspecifications persist?

We use an evolutionary model to determine which misperceptions can persist. Every period, a new generation of agents use their subjective models and the data generated by the previous generation to update their beliefs, and models that induce better actions become more prevalent. An equilibrium can resist mutations that lead agents to use a model that better fits the equilibrium data but induce the mutated agents to take an action with lower payoffs. We characterize which steady states resist mutations to a nearby model, and which resist mutations that drop a qualitative restriction such as independence.

Accounting conservatism and relational contracting

This paper develops a positive role for accounting conservatism in fostering relational contracts between two agents in a two-period model of moral hazard. Building on Kreps (1996), the principal in our model designs a conservative measurement system and optimal contracts to create multiple equilibria that foster a team-based corporate culture. Accruals introduced by conservatism increase each agent's stake in the future of the relationship when it matters most—when it is going badly. This makes staying in the relationship worthwhile for the agents, even if they plan to play a low payoff equilibrium in the second period to punish first-period free-riding. In turn, this allows the principal to use lower-powered (and less costly) team incentives in the first period of the relationship. In contrast, deferred compensation increases each agent's stake in the future of the relationship when it is going well, making it less efficient in fostering relationships.

How Fast Do Investors Learn? Asset Management Investors and Bayesian Learning

Abstract We study the speed with which investors learn about managers’ skills by examining how quickly investor and managers’ beliefs converge. After showing our measure proxies for the change in the dispersion of beliefs, we find that hedge fund investors learn as fast as suggested by Bayes’ rule. However, we find mutual fund investors learn more slowly than suggested by Bayes’ rule. Mutual fund investors’ slow learning is not due to the use of different performance measures, institutional frictions, or lack of sophistication, but could be due to a low payoff from learning. Our results indicate learning speed depends on financial participants’ incentives. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Don't shoot yourself in the foot! A (real-effort task) experiment on income redistribution and voting

This paper reports results from a laboratory experiment that investigates the Meltzer–Richard model of equilibrium tax rates in which individuals are either low or high skilled workers and face a real-effort task that includes leisure at the work place. We find that a large proportion of low-skilled workers vote for the lowest tax rate (the one that gives them the lowest payoff), especially when the alternative tax rate is very high. However, this proportion is significantly reduced in treatments in which the subjects are given extra information about how the tax operates in redistributing income. This result suggests that the lack of information about the role of taxes in income redistribution may be an important factor in explaining the counter-intuitive voting behavior of low-income voters over income redistribution. We also find some support that the prospect of upward mobility and the belief in the negative effect of taxes on productivity make low-income voters support low tax rates, especially when the alternative tax rate is very high.

Managing product upgrades and rollover under demand uncertainty

We study the optimal product upgrades and rollover strategies of a risk-averse firm that is uncertain about future demand. For this purpose, we develop a two-period model based on whether the firm makes upgrading investments and if so which product rollover (solo or dual) strategy it adopts. Analysis of the equilibrium outcomes shows that if the firm is moderately risk-averse, it is unprofitable to upgrade and therefore only sells the first-generation product over two periods. Otherwise, the firm benefits from upgrading investments. In this case, the (solo-) dual-rollover guarantees the maximum total payoff if the degree of risk aversion is (low) high. Our sensitivity analysis demonstrates that: (i) the dual-rollover strategy can be seen as a hedge against increased demand uncertainty; (ii) the firm has a higher likelihood of using the dual-rollover strategy as cannibalization intensifies or intertemporal demand spillovers increase; and (iii) a lower payoff discount rate generally discourages the firm from upgrading the product. When upgrading investments happen, the optimal product rollover strategy is contingent upon the degree of risk aversion and the payoff discount rate.

Rewards for information provision in patient referrals: A theoretical model and an experimental test

We study whether bonus payments for information provision can improve the information flow between physicians. A primary care physician (PCP) decides on the provision of information of varying qualities to a specialist while referring a patient. Our theoretical model, which includes altruism and loss aversion, predicts that bonus payments increase the provision of both high- and low-quality information. Running a controlled laboratory experiment we find support for this prediction. If the beneficiary of information provision receives a higher payoff than the PCP, we observe that PCPs more often pass on high-quality information when the beneficiary is a patient. If the beneficiary receives a lower payoff than the PCP, the type of the beneficiary (specialist or patient) does not affect the provision of high-quality information.

‘What is important is seldom urgent and what is urgent is seldom important’: a study of the strategic implications of the urgency effect in a competitive setting

The urgency effect refers to people’s tendency to choose a relatively unimportant task (with unambiguously low payoff) over a relatively important task (with unambiguously high payoff), when the former is spuriously framed as urgent. In this paper I study a simple model in which two payoff-maximising task suppliers compete for a population of heterogeneous decision-makers. Task suppliers offer tasks of various importance, and can exert costly effort to manipulate the perceived urgency of the offered tasks. Decision-makers are of two kinds: they either choose more important over less important tasks by disregarding the urgency frames (fully rational) or behave like fully rational decision-makers, except that they are subject to the urgency effect (boundedly rational). I study the unique symmetric equilibrium of the resulting game and derive the conditions under which the urgency effect has detrimental effects on the decision-makers’ welfare. Furthermore, I examine the implications of several policies aimed at correcting the failure, which include educating boundedly rational decision-makers and auditing task suppliers that use urgency framing.

Hypoxia and risk preferences: Mild hypoxia impacts choices for low-probability high-payoff bets.

Mild degrees of hypoxia are known to exert a detrimental effect on cognitive functions. In a lab study, we assessed the effect of mild hypoxia on risk-taking behavior. Participants (N = 25) were presented with pairs of bets of equal expected monetary value, one having a higher probability of winning/losing a lower payoff (safer bet) and one having a lower probability of winning/losing a higher payoff (riskier bet). We systematically varied the ratio of the probabilities (and corresponding payoffs) of the two bets and examined how this affected participants’ choice between them. Following a familiarization session, participants performed the task twice: once in a normoxic environment (20.9% oxygen concentration) and once in a mildly hypoxic environment (14.1% oxygen concentration). Participants were not told and could not guess which environment they were in. We found a higher preference for the riskier bet in the mild hypoxic than normoxic environment but only in the loss domain. Furthermore, as the probability ratio increased, mild hypoxia increased the preference for the riskier bet in the domain of losses but decreased it for gains. The present findings support that mild hypoxia promotes riskier choices in the loss domain and provide new insights into the impact of mild hypoxia in moderating the effect of probability ratio on risky choices.

Equity Issuance Methods and Dilution

Abstract We analyze rights and public offerings when informed shareholders strategically choose to subscribe. Absent wealth constraints, rights offerings achieve the full information outcome and dominate public offerings. When some shareholders are wealth constrained, rights offerings lead to more dilution of their stakes and lower payoffs, despite the income from selling these rights. In both rights and public offerings, there is a trade-off between investment efficiency and wealth transfers among shareholders. When firms can choose the flotation method, either all firms choose the same offer method or high and low types opt for rights offerings, while intermediate types select public offerings. (JEL G32)

Reputation Building under Observational Learning

Abstract A patient seller interacts with a sequence of myopic consumers. Each period, the seller chooses the quality of his product, and a consumer decides whether to trust the seller after she observes the seller’s actions in the last $K$ periods (limited memory) and at least one previous consumer’s action (observational learning). However, the consumer cannot observe the seller’s action in the current period. With positive probability, the seller is a commitment type who plays his Stackelberg action in every period. I show that under limited memory and observational learning, consumers are concerned that the seller will not play his Stackelberg action when he has a positive reputation and will play his Stackelberg action after he has lost his reputation. Such a concern leads to equilibria where the seller receives a low payoff from building a reputation. I also show that my reputation failure result hinges on consumers’ observational learning.

Network Characteristic Control of Social Dilemmas in a Public Good Game: Numerical Simulation of Agent-Based Nonlinear Dynamics

This paper proposes a possible mechanism for obtaining sizeable behavioral structures by simulating a network–agent dynamic on an evolutionary public good game with available social .learning. The model considers a population with a fixed number of players. In each round, the chosen players may contribute part of their value to a common pool. Then, each player may imitate the strategy of another player based on relative payoffs (whoever has the lower payoff adopts the strategy of the other player) and change his or her strategy using different exploratory variables. Relative payoffs are subject to incentives, including participation costs, but may also be subject to mutation, whose rate is sensitized by the network characteristics (social ties). The process discussed in this report is interesting and relevant across a broad range of disciplines that use game theory, including cultural evolutionary dynamics.