Reservation Value Research Articles

Analysis Of Future Health Insurance Premium Reserve Calculations Using The Commissioners Method With Woolhouse Formula

A premium reserve is the amount of funds that the insurance company needs to prepare for the payment of liability benefits when a claim occurs. One method of calculating premiums is the commissioners method which is an extension of the prospective reserve method.The main factor in the actuarial calculation is the mortality rate that can be determined using the WOOLHOUSE mortality law. This study aims to determine the size of the life insurance premiums reserve using the commisioners method and the WOLHOUSE mortality laws. The calculation of the premium reserve is linked to the determination of a person's chances of survival over a period of years of WOALHOUSE law which is then used to find the value of the insurance, the initial annuity value, the annual premium, the modified premiums based on the Commissioners method, and the amount of the premie reserve at the end of the year. The study was conducted on a 25-year-old woman who was enrolled in a dwiguna life insurance program with a 25 year liability period and a 23 year premium payment period at a 4% interest rate with a liability of Rs. 500,000,000. The results of the analysis showed that the large reserves of premiums obtained at the end of the period of liability with the Commissioners method and the WOOLHOUSE mortality law are equal to the given reservation value, so that the insurance company is prepared to give the amount of reservation promised to the policyholder.

Contextual Pandora’s Box

Pandora’s Box is a fundamental stochastic optimization problem, where the decision-maker must find a good alternative, while minimizing the search cost of exploring the value of each alternative. In the original formulation, it is assumed that accurate distributions are given for the values of all the alternatives, while recent work studies the online variant of Pandora’s Box where the distributions are originally unknown. In this work, we study Pandora’s Box in the online setting, while incorporating context. At each round, we are presented with a number of alternatives each having a context, an exploration cost and an unknown value drawn from an unknown distribution that may change at every round. Our main result is a no-regret algorithm that performs comparably well against the optimal algorithm which knows all prior distributions exactly. Our algorithm works even in the bandit setting where the algorithm never learns the values of the alternatives that were not explored. The key technique that enables our result is a novel modification of the realizability condition in contextual bandits that connects a context to a sufficient statistic of each alternative’s distribution (its reservation value) rather than its mean.

Male investment in schooling with frictional labour and marriage markets

We present an equilibrium model with inter-linked frictional labour and marriage markets. Women’s flow value of being single is treated as given, and it captures returns from employment. Men can undertake a costly ex-ante investment in schooling. In the marriage market, women search sequentially for men characterised by wages, so they use a reservation value strategy. Single unemployed men conduct marital sequential search and, with an eye on the marriage market, also conduct a so-called constrained sequential job search. Given this setup, schooling enhances men’s marriage prospects as well as their labour market returns. In turn, women’s behaviour affects men’s schooling investment decision and their optimal job search strategy. We establish that for any given set of parameters, there exists a unique market equilibrium where a fraction of men get educated, and show that this fraction decreases if women’s labour market returns increase. We also examine the robustness of such an equilibrium.

Competitive information disclosure in random search markets

We analyze the role of competition in information provision in random search markets. Multiple symmetric senders compete for the receiver's investment by disclosing information about their respective project qualities, and the receiver conducts random search to learn about the qualities of the projects. We show that in any symmetric pure strategy Nash equilibrium, each sender chooses a strategy with the lowest possible reservation value. There is no active search, and the receiver does not benefit from the competition of the senders.

Loss Aversion and Seller’s Reservation Value in the Housing Market

Loss Aversion and Seller’s Reservation Value in the Housing Market

Research on Fast and Precise Positioning Strategy of an Ultrasonic Motor Based on the Ultrasonic Friction Reduction Theory.

To address the problems of the large positioning error and long positioning time of the traditional positioning strategy, namely, the two-phase simultaneous power-off method (TPSPM), a new positioning strategy, called the first single-phase then two-phase power-off method (FSPTTPPM), based on the ultrasonic friction reduction theory, has been proposed in this work. This method realizes zero sliding displacement between the friction material and the stator during the torsional oscillation of the shaft by controlling the driving circle frequency and the duration of the single-phase power-off period, which reduces the deviation of the displacement reservation value. In order to verify the correctness of the driving mechanism, a test platform has been built, and two positioning strategies have been used for experimental verification. The following experimental results have been obtained: compared to TPSPM, FSPTTPPM has the advantages of higher positioning accuracy and short positioning time. In terms of the positioning accuracy, the relative errors of the displacement reservation values of FSPTTPPM and TPSPM vary with the initial angular velocity (0.24 to 1.18 rad/s) in the range of −0.4 to 0.1 and −0.8 to 0.8, respectively. In addition, the relative error of the displacement reservation value is closer to zero than that of TPSPM at the same initial angular velocity. In terms of the positioning time, when the initial angular velocity is greater than 0.7 rad/s, the positioning time of the FSPTTPPM is approximately 10 ms smaller than that of the TPSPM.

Pandora’s Box Problem with Order Constraints

The Pandora’s Box problem, originally posed by Weitzman in 1979, models selection from a set of random-valued alternatives—the “boxes”—when evaluation is costly. Weitzman showed that the Pandora’s Box problem admits a simple threshold-based solution that considers the options in decreasing order of reservation value, a proxy for the actual value of the boxes in the exploration process. We study for the first time this problem when the order in which the boxes are opened is constrained, forcing the solution to account for both the depth of search, as opening a box gives access to more boxes, and the breadth, as there are many directions to explore. Despite these difficulties, we show that greedy optimal strategies exist and can be efficiently computed for tree-like order constraints. We also prove that finding optimal adaptive search strategies is NP-hard to approximate (up to a certain constant) when certain matroid constraints are applied to further restrict the set of boxes that may be opened or when the order constraints are given as reachability constraints on a directed acyclic graph. We complement this hardness result by giving efficient approximation algorithms, exploiting a low adaptivity gap for a carefully relaxed version of the problem. Funding: This work was supported by the National Science Foundation [Grant 1750436] and the Ministero dell'Istruzione, dell'Università e della Ricerca [PRIN. ALGADIMAR “Algorithms, Games, and Digital]. This work was also supported by the ERC Advanced [Grant 788893] Algorithmic and Mechanism Design Research in Online Markets (AMDROMA).

Financing land acquisition for infrastructure projects

Land acquisition for infrastructure projects that require a large amount of funding can be financed with an equity-like protocol. The auction protocol does not require knowledge of the reservation value of the land acquired, nor does it require determination of the post-development value of the land in the surrounding area. Competition among private players transfers the value of pecuniary externalities, manifested in land price appreciation, to the government, which it can use to partially finance the project.

Driving a hard bargain is a balancing act: how social preferences constrain the negotiation process

We investigate the haggling process in bargaining. Using an experimental bargaining game, we find that a first offer has a significant impact on the bargaining outcome even if it is costless to reject. First offers convey information on the player’s reservation value induced by his social preferences. They are most often accepted when they are not above the equal split. However, offers which request much more than the equal split induce punishing counter-offers. The bargaining outcome is therefore critically influenced by the balance of toughness and kindness signalled through the offers made in the haggling phase.

Blending Capacity on a Rideshare Platform: Independent and Dedicated Drivers

A rideshare platform acts as an aggregator that connects riders with ride providers (drivers). The drivers are independent workers who share a part of their revenue with the principal, who owns the platform. While drivers have flexible schedules, the fairness of labor contracts and control exercised by the principal have come into question lately. Suggested options include treating the drivers as employees and/or safeguarding a minimum income for them. We study a rideshare platform with blended driver capacity: full time employees with a fixed wage rate, and independent drivers who are paid a share of revenue. We examine a scenario where the principal establishes the number of employee drivers, revenue sharing, and a base price for the platform; and the independent drivers then determine whether to join the platform. We identify economic equilibrium for two different demand rationing strategies: preference for employee drivers, and equal opportunity for all drivers (driver‐agnostic). We find that a blended platform capacity becomes viable if the wage rate is moderate, pool of independent drivers is large, and the ride‐seeker market is large. We show that the unpredictability of driver's reservation value motivates the principal to hire more employee drivers and to increase the base price. Our result that a driver‐agnostic demand rationing causes fewer independent drivers to join the platform is somewhat counterintuitive and is explained by how revenue sharing affects demand rationing. We find that the ride seekers prefer preferential demand rationing over driver‐agnostic rationing.

Does Internet Connectedness Disconnect Marriage? A Micro Empirical Analysis

This study explores the relationship between internet use during non-working hours and marriage well-being and channels through which internet use operates on marital satisfaction. With a 2-year nationwide micro panel data, our main results reveal negative effects of internet experience on overall marriage satisfaction, satisfaction towards spousal contribution in housework and marital stability. Empirically, we adopt linear as well as nonlinear models, use propensity score matching approach, and implement parametric as well as semiparametric analyses. Evidence further show that active internet users can use the internet to chat with strangers and easily access potential romantic partners. Its social function leads to a substantial reduction in search cost and raised reservation value of partner contribute to a lower level of spousal satisfaction. Moreover, it was also found that internet use partially weakens traditional Chinese views of family gender roles. And gender ideology changes through internet’s educational function has increased spousal dissatisfaction in China. In addition, it is found that internet use crowds out time spent on housework as well as other investment in current marriage, and hence increases spousal dissatisfaction.

Gacha Game: Selling a Unit Good to a Prospect Theory Consumer

This paper considers the design problem of selling a unit good to a prospect theory buyer, with non-negative constraints on the realized price. When the value is private and the reservation value is 0, it is optimal for the seller to use a post binary random price mechanism, where he charges a large price that may exceed the buyer's actual value and gives a full refund with some probability. When the reservation value is positive, the seller may provide infinite menus to different types of buyers. Each menu consists of a binary random price and a (potentially) interior probability of getting the good. If the buyer is naive about her dynamic inconsistent preference caused by probability weighting, the seller can potentially gain more profit from a dynamic pricing process. When the buyer's value is public, the generically unique optimal dynamic pricing strategy is to sell a ``lucky chest'' that delivers the good with some constant probability in each period. Until she finally gets the good, the buyer always naively believes she will try her luck just one last time.

Observational Learning and Information Disclosure in Search Markets

This paper studies the role of observational learning in search markets where buyers do not take the list price as a take-it-or-leave-it offer. Using a unique data from the Beijing housing market, we estimate a structural model in which buyers infer a seller’s reservation value from the home’s list price, time-on-market, and records of in-person home viewings by prior prospective buyers, after which they decide whether to view the home and how much to offer. We use the estimated model to quantify the welfare impact of different information disclosure rules. We find that buyer surplus is reduced, and seller surplus is increased on average if time-on-market information is disclosed. However, disclosing home-viewing information in addition to time-on-market information affects individual homes differently. We find that due to the disclosure of this additional information, buyers are slightly better off while sellers are slightly worse off on average.

Endogenizing the Reservation Value in Models of land Development over Time and Under Uncertainty Revisited

Endogenizing the Reservation Value in Models of land Development over Time and Under Uncertainty Revisited

The importance of memory for price discovery in decentralized markets

We study the dynamics of price discovery in decentralized two-sided markets. We show that there exist memoryless dynamics that converge to the core of the underlying assignment game in which agents' actions depend only on their current payoff. However, we show that for any such dynamic the convergence time can grow exponentially in relation to the population size. We present a natural dynamic in which a player's reservation value provides a summary of his past information and show that this dynamic converges to the core in polynomial time in homogeneous markets.

Efficient Price Discovery and Information in the Decentralized Assignment Game

We study the dynamics of price discovery in decentralized two-sided markets. There exist memoryless dynamics that converge to the core in which agents' actions depend only on their current payoff. However, we show that for any such dynamic the convergence time can grow exponentially in the population size. We present a natural dynamic in which a player's reservation value provides a summary of her past information and show that this dynamic converges to the core in polynomial time in homogeneous markets.

A Hybrid Concession Mechanism for Negotiating Software Agents in Competitive Environments

This paper presents a new hybrid concession mechanism for negotiating agents. It considers both the current concession behavior of the proposing agent and the concession offered by its opponent in the last counteroffer to create a new offer. The proposed mechanism is a kind of imitating offer generation tactic. The difference is that it uses the first order difference between the two last counteroffers received from the opponent as its current reservation value which is one of the important inputs in generating a new offer. In this paper, a bilateral negotiation over a single issue is considered where agents have adverse interests over the issue such as price. Four negotiation environmental settings are used to test the proposed offer generating mechanism. The experimental results show that the proposed hybrid concession mechanism outperforms the time-dependent concession tactic in terms of utility rate while performing lower in one negotiation environment and similarly in most of negotiation environments.

Is Simplicity the Ultimate Sophistication? The Superiority of Linear Pricing

We consider a supply chain with a supplier selling products to a retailer who is boundedly rational. The retailer’s orders are randomly distributed around the optimal order quantity. We develop a behavioral model which incorporates human retailers’ bounded rationality in the supplier’s contractual decisions. In contrast to a supply chain with a fully rational retailer, where a wholesale price contract usually cannot outperform more complicated nonlinear contracts, we find that when the retailer is boundedly rational a wholesale price contract can dominate commonly used nonlinear contracts, such as buyback and revenue sharing contracts, in terms of a supplier’s profit and supply chain profit. We characterize the conditions under which a wholesale price contract outperforms more sophisticated nonlinear contracts for the supplier. In particular, we show that a wholesale price contract is more likely to be implemented by the supplier when the supply chain profit margin is low, the retailer is less rational, the demand variance is large, and the retailer’s reservation value is high. We then conduct a series of laboratory experiments to test whether the behavioral model’s predictions are still salient even when the supplier is not necessarily rational. Our results provide an explanation for the prevalence of wholesale price contracts in business practice where the rationality of a retailer cannot always be guaranteed. We also find that a retailer’s bounded rationality plays a more important role in determining supply chain profit than a supplier’s bounded rationality.

Learning while shopping: an experimental investigation into the effect of learning on consumer search.

In many search environments, searchers are learning about the distribution of offers in the market. I conduct an experiment exploring a broad class of search problems with learning about the distribution of payoffs. My results support the prediction that learning results in declining reservation values, providing evidence that learning may be an explanation for recall. Theory predicts a “one step” reservation value strategy, but many subjects instead choose to set a high reservation value in order to learn about the distribution before adjusting based on their observations. Under-searching in search experiments may stem from a reinforcement heuristic and lack of negative feedback after using sub-optimal strategies.Electronic supplementary materialThe online version of this article (10.1007/s10683-020-09659-7) contains supplementary material, which is available to authorized users.

Competitive Revenue Management with Sequential Bargaining

When firms post prices to sell their products in a competitive market, buyers often seek to bargain down the prices. The existing studies on dynamic competition, however, focus on firms’ dynamic pricing strategies without considering the possibility of bargaining. We model a random stream of buyers with heterogeneous valuations who may choose to negotiate for a discount from a posted price. When bargaining is allowed, a seller firm's competing strategy depends not only on her reservation value (i.e., her gain from an unsold item when losing the current buyer to the opponent) but also on her disagreement point (i.e., the value of an unsold item when the negotiation with an arriving buyer breaks down). We show that the reservation values and the disagreement points can play opposite roles in competition—the seller firms’ posted prices are increasing in their reservation values but are decreasing in their disagreement points. In general, a seller becomes more aggressive in price competition when her reservation value becomes lower. However, it is not always the case that a seller with a lower reservation value can successfully win the deal from an arriving buyer, as it is in pure price competition. Because of the possibility of bargaining, the buyer may end up purchasing from a seller who has a higher inventory level and a higher reservation value when the seller's disagreement point is lower than that of her opponent. Interestingly, such an equilibrium outcome can only arise when the selling season is sufficiently long. Our analysis highlights the intriguing role played by negotiation in dynamic competition for sequential selling.