Michal Lewandowski - Academia.edu (original) (raw)
Papers by Michal Lewandowski
Przegląd Statystyczny, 2021
We optimise a postal delivery problem with time and capacity constraints imposed on vehicles and ... more We optimise a postal delivery problem with time and capacity constraints imposed on vehicles and nodes of the logistic network. Time constraints relate to the duration of routes, whereas capacity constraints concern technical characteristics of vehicles and postal operation outlets. We consider a method which can be applied to a brownfield scenario, in which capacities of outlets can be relaxed and prospective hubs identified. As a solution, we apply a genetic algorithm and test its properties both in small case studies and in a simulated problem instance of a larger (i.e. comparable with real-world instances) size. We show that the genetic operators we employ are capable of switching between solutions based on direct origin-to-destination routes and solutions based on transfer connections, depending on what is more beneficial in a given problem instance. Moreover, the algorithm correctly identifies cases in which volumes should be shipped directly, and those in which it is optimal ...
Central European Journal of Economic Modelling and Econometrics, 2013
Journal of Risk and Uncertainty, Jun 1, 2014
I analyze two expected utility models which abandon the consequentialist assumption of terminal w... more I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281-1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms. Keywords Expected utility • Narrow framing • Rabin (2000) paradox • Preference reversal • WTA/WTP disparity • Buying and selling price for a lottery JEL Classifications D81 • D03 • C91 Willingness to accept (WTA) or selling price for a lottery is a minimal sure amount of money which a person is willing to accept to forego the right to play the lottery. Willingness to pay (WTP) or buying price for a lottery, on the other hand, is a maximal sure amount of money which a person is willing to pay in order to get the right to play the lottery. The disparity between willingness to pay and willingness to accept is a well-known phenomenon that arises in experimental settings. There is a large body of evidence starting with Knetsch and Sinden (1984) and Thaler (1980) that WTA is much higher than WTP for many types of goods. Horowitz and McConnell (2002)
Theory and Decision
Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health p... more Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health preference research. However, DCEs only provide binary responses, whilst real-life choices are made with varying degrees of conviction. We aimed to verify whether eliciting self-reported convictions on a 0–100 scale adds meaningful information to the binary choice. Eighty three respondents stated their preferences for health states using DCE and the time trade-off method (TTO). In TTO, utility ranges were also elicited to account for preference imprecision. We verified the properties of the conviction across three areas: (1) response to various choice task modifications (e.g. dominance, increase in complexity, distance from the status quo) and association with rationality violations (e.g. intransitivity); (2) association with test–retest results; (3) relation to the utility difference and imprecision estimated in TTO. Regarding (1), conviction increased in choice tasks with lower complexi...
The main focus of this tutorial/review is on presenting Prospect Theory in the context of the sti... more The main focus of this tutorial/review is on presenting Prospect Theory in the context of the still ongoing debate between the behavioral (mainly descriptive) and the classical (mainly normative) approach in decision theory under risk and uncertainty. The goal is to discuss Prospect Theory vs. Expected Utility in a comparative way. We discuss: a) which assumptions (implicit and explicit) of the classical theory are being questioned in Prospect Theory; b) how does the theory incorporate robust experimental evidence, striving, at the same time, to find the right balance between the basic rationality postulates of Expected Utility (e.g. monotonicity wrt. First-Order Stochastic Dominance), psychological plausibility and mathematical elegance; c) how are risk attitudes modeled in the theory. In particular we discuss prospect stochastic dominance and the three-pillar structure of modeling risk attitudes in Prospect Theory involving: the non-additive decision weights with lower and upper s...
We build upon Goeree and Holt [American Economic Review, 91 (5) (2001), 1402-1422] and show that ... more We build upon Goeree and Holt [American Economic Review, 91 (5) (2001), 1402-1422] and show that the departures from Nash Equilibrium predictions observed in their experiment on static games of complete information can be explained by minimizing the maximum regret.
Rabin and Thaler (2001) declared Expected Utility an ex-hypothesis or a dead parrot alluding to t... more Rabin and Thaler (2001) declared Expected Utility an ex-hypothesis or a dead parrot alluding to the famous sketch from Monthy Pythons Flying Circus. Following Cox and Sadiraj (2006) and others, one should distinguish between Expected Utility (EU) theory (a purely mathematical theory based on axioms) and Expected Utility models (EU theory plus a given economic interpretation). The most prevalent EU model is one that assumes consequentialism (Rubinstein, 2012). Consequentialism states that the decision maker has a single binary preference relation comparing probability distributions over final wealth levels. Preference relations over wealth changes for different levels of wealth are derived from this single preference relation. EU theory plus consequentialism is referred to as the standard EU model. It is argued that most of the critique against EU is against the standard EU model, or against consequentialism. We replace consequentialism with reference-dependence, retaining the EU hyp...
Behavioral & Experimental Economics eJournal, 2020
This paper reevaluates the complementary symmetry hypothesis and the supporting experimental evid... more This paper reevaluates the complementary symmetry hypothesis and the supporting experimental evidence. Originally the hypothesis was stated for binary risky prospects. We generalize the hypothesis to arbitrary state-contingent real-valued acts, thus extending the domain from risk to uncertainty/ambiguity and allowing for multiple outcomes. Existing experiments tested the hypothesis using selling and buying prices and found systematic violations. We argue that in order to be consistent with the hypothesis one should replace selling with short-selling. We thus define a new elicitation task and run an experiment to test our conjecture. We replicate previously observed violations in the old setting and find strong support for the hypothesis in the new setting. In addition, our results shed new light on the validity of various reference point setting rules.
This paper establishes a number of functional relationships between the riskiness measure of Fost... more This paper establishes a number of functional relationships between the riskiness measure of Foster-Hart and its extension and buying/selling price of a lottery. The results allow comparison of riskiness measures for lotteries that either have non-positive expectation or do not take negative values.
This paper defines the concept of simple strategy and introduces three kinds of simple strategies... more This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the corresponding simple strategy, in terms of the buying and selling price properties, and in terms of the utility function properties as expressed by Cauchy functional equations. Moreover, an extension of famous Pratt (1964) theorem is proved which involves buying price for a lottery as an alternative measure of comparative risk aversion. Additionally a number of propositions on both selling and buying price for a lottery and CRRA utility class are proved.
Journal of Mathematical Psychology
It is shown that complementary symmetry holds in Cumulative Prospect Theory with random reference... more It is shown that complementary symmetry holds in Cumulative Prospect Theory with random reference if the utility function for gains and losses is strictly increasing and continuous. Previous results imposed more restrictions involving preference homogeneity, reflection, and loss aversion. The result holds true in the general version of the Third-Generation Prospect Theory provided that the relative value function v takes the same form as in Cumulative Prospect Theory.
Transitivity and independence are necessary to guarantee no-arbitrage.
SSRN Electronic Journal, 2000
In this paper I analyze operational measure of riskiness defined by . I give simple intuition beh... more In this paper I analyze operational measure of riskiness defined by . I give simple intuition behind their main result.
SSRN Electronic Journal, 2000
I analyze two expected utility models which abandon the consequentialist assumption of terminal w... more I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281-1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms.
SSRN Electronic Journal, 2000
This paper defines the concept of simple strategy and introduces three kinds of simple strategies... more This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the corresponding simple strategy, in terms of the buying and selling price properties, and in terms of the utility function properties as expressed by Cauchy functional equations. Moreover, an extension of famous Pratt (1964) theorem is proved which involves buying price for a lottery as an alternative measure of comparative risk aversion. Additionally a number of propositions on both selling and buying price for a lottery and CRRA utility class are proved.
SSRN Electronic Journal, 2000
The paper proposes a behavioral decision rule for choice under risk. This rule is designed to exp... more The paper proposes a behavioral decision rule for choice under risk. This rule is designed to explain patterns of behavior in two paradoxes of classic decision theory i.e. Asian disease paradox and preference reversal puzzle. The loss aversion which is the driving force of this explanation is captured in the W T A/W T P disparity. The proposed decision rule is then showed to be equivalent to decision-making in the Cumulative Prospect Theory with appropriately chosen quasi-endogenous reference points.
SSRN Electronic Journal, 2000
Przegląd Statystyczny, 2021
We optimise a postal delivery problem with time and capacity constraints imposed on vehicles and ... more We optimise a postal delivery problem with time and capacity constraints imposed on vehicles and nodes of the logistic network. Time constraints relate to the duration of routes, whereas capacity constraints concern technical characteristics of vehicles and postal operation outlets. We consider a method which can be applied to a brownfield scenario, in which capacities of outlets can be relaxed and prospective hubs identified. As a solution, we apply a genetic algorithm and test its properties both in small case studies and in a simulated problem instance of a larger (i.e. comparable with real-world instances) size. We show that the genetic operators we employ are capable of switching between solutions based on direct origin-to-destination routes and solutions based on transfer connections, depending on what is more beneficial in a given problem instance. Moreover, the algorithm correctly identifies cases in which volumes should be shipped directly, and those in which it is optimal ...
Central European Journal of Economic Modelling and Econometrics, 2013
Journal of Risk and Uncertainty, Jun 1, 2014
I analyze two expected utility models which abandon the consequentialist assumption of terminal w... more I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281-1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms. Keywords Expected utility • Narrow framing • Rabin (2000) paradox • Preference reversal • WTA/WTP disparity • Buying and selling price for a lottery JEL Classifications D81 • D03 • C91 Willingness to accept (WTA) or selling price for a lottery is a minimal sure amount of money which a person is willing to accept to forego the right to play the lottery. Willingness to pay (WTP) or buying price for a lottery, on the other hand, is a maximal sure amount of money which a person is willing to pay in order to get the right to play the lottery. The disparity between willingness to pay and willingness to accept is a well-known phenomenon that arises in experimental settings. There is a large body of evidence starting with Knetsch and Sinden (1984) and Thaler (1980) that WTA is much higher than WTP for many types of goods. Horowitz and McConnell (2002)
Theory and Decision
Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health p... more Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health preference research. However, DCEs only provide binary responses, whilst real-life choices are made with varying degrees of conviction. We aimed to verify whether eliciting self-reported convictions on a 0–100 scale adds meaningful information to the binary choice. Eighty three respondents stated their preferences for health states using DCE and the time trade-off method (TTO). In TTO, utility ranges were also elicited to account for preference imprecision. We verified the properties of the conviction across three areas: (1) response to various choice task modifications (e.g. dominance, increase in complexity, distance from the status quo) and association with rationality violations (e.g. intransitivity); (2) association with test–retest results; (3) relation to the utility difference and imprecision estimated in TTO. Regarding (1), conviction increased in choice tasks with lower complexi...
The main focus of this tutorial/review is on presenting Prospect Theory in the context of the sti... more The main focus of this tutorial/review is on presenting Prospect Theory in the context of the still ongoing debate between the behavioral (mainly descriptive) and the classical (mainly normative) approach in decision theory under risk and uncertainty. The goal is to discuss Prospect Theory vs. Expected Utility in a comparative way. We discuss: a) which assumptions (implicit and explicit) of the classical theory are being questioned in Prospect Theory; b) how does the theory incorporate robust experimental evidence, striving, at the same time, to find the right balance between the basic rationality postulates of Expected Utility (e.g. monotonicity wrt. First-Order Stochastic Dominance), psychological plausibility and mathematical elegance; c) how are risk attitudes modeled in the theory. In particular we discuss prospect stochastic dominance and the three-pillar structure of modeling risk attitudes in Prospect Theory involving: the non-additive decision weights with lower and upper s...
We build upon Goeree and Holt [American Economic Review, 91 (5) (2001), 1402-1422] and show that ... more We build upon Goeree and Holt [American Economic Review, 91 (5) (2001), 1402-1422] and show that the departures from Nash Equilibrium predictions observed in their experiment on static games of complete information can be explained by minimizing the maximum regret.
Rabin and Thaler (2001) declared Expected Utility an ex-hypothesis or a dead parrot alluding to t... more Rabin and Thaler (2001) declared Expected Utility an ex-hypothesis or a dead parrot alluding to the famous sketch from Monthy Pythons Flying Circus. Following Cox and Sadiraj (2006) and others, one should distinguish between Expected Utility (EU) theory (a purely mathematical theory based on axioms) and Expected Utility models (EU theory plus a given economic interpretation). The most prevalent EU model is one that assumes consequentialism (Rubinstein, 2012). Consequentialism states that the decision maker has a single binary preference relation comparing probability distributions over final wealth levels. Preference relations over wealth changes for different levels of wealth are derived from this single preference relation. EU theory plus consequentialism is referred to as the standard EU model. It is argued that most of the critique against EU is against the standard EU model, or against consequentialism. We replace consequentialism with reference-dependence, retaining the EU hyp...
Behavioral & Experimental Economics eJournal, 2020
This paper reevaluates the complementary symmetry hypothesis and the supporting experimental evid... more This paper reevaluates the complementary symmetry hypothesis and the supporting experimental evidence. Originally the hypothesis was stated for binary risky prospects. We generalize the hypothesis to arbitrary state-contingent real-valued acts, thus extending the domain from risk to uncertainty/ambiguity and allowing for multiple outcomes. Existing experiments tested the hypothesis using selling and buying prices and found systematic violations. We argue that in order to be consistent with the hypothesis one should replace selling with short-selling. We thus define a new elicitation task and run an experiment to test our conjecture. We replicate previously observed violations in the old setting and find strong support for the hypothesis in the new setting. In addition, our results shed new light on the validity of various reference point setting rules.
This paper establishes a number of functional relationships between the riskiness measure of Fost... more This paper establishes a number of functional relationships between the riskiness measure of Foster-Hart and its extension and buying/selling price of a lottery. The results allow comparison of riskiness measures for lotteries that either have non-positive expectation or do not take negative values.
This paper defines the concept of simple strategy and introduces three kinds of simple strategies... more This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the corresponding simple strategy, in terms of the buying and selling price properties, and in terms of the utility function properties as expressed by Cauchy functional equations. Moreover, an extension of famous Pratt (1964) theorem is proved which involves buying price for a lottery as an alternative measure of comparative risk aversion. Additionally a number of propositions on both selling and buying price for a lottery and CRRA utility class are proved.
Journal of Mathematical Psychology
It is shown that complementary symmetry holds in Cumulative Prospect Theory with random reference... more It is shown that complementary symmetry holds in Cumulative Prospect Theory with random reference if the utility function for gains and losses is strictly increasing and continuous. Previous results imposed more restrictions involving preference homogeneity, reflection, and loss aversion. The result holds true in the general version of the Third-Generation Prospect Theory provided that the relative value function v takes the same form as in Cumulative Prospect Theory.
Transitivity and independence are necessary to guarantee no-arbitrage.
SSRN Electronic Journal, 2000
In this paper I analyze operational measure of riskiness defined by . I give simple intuition beh... more In this paper I analyze operational measure of riskiness defined by . I give simple intuition behind their main result.
SSRN Electronic Journal, 2000
I analyze two expected utility models which abandon the consequentialist assumption of terminal w... more I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281-1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms.
SSRN Electronic Journal, 2000
This paper defines the concept of simple strategy and introduces three kinds of simple strategies... more This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the corresponding simple strategy, in terms of the buying and selling price properties, and in terms of the utility function properties as expressed by Cauchy functional equations. Moreover, an extension of famous Pratt (1964) theorem is proved which involves buying price for a lottery as an alternative measure of comparative risk aversion. Additionally a number of propositions on both selling and buying price for a lottery and CRRA utility class are proved.
SSRN Electronic Journal, 2000
The paper proposes a behavioral decision rule for choice under risk. This rule is designed to exp... more The paper proposes a behavioral decision rule for choice under risk. This rule is designed to explain patterns of behavior in two paradoxes of classic decision theory i.e. Asian disease paradox and preference reversal puzzle. The loss aversion which is the driving force of this explanation is captured in the W T A/W T P disparity. The proposed decision rule is then showed to be equivalent to decision-making in the Cumulative Prospect Theory with appropriately chosen quasi-endogenous reference points.
SSRN Electronic Journal, 2000