arXiv subjects

Irit Nowik

Publications and source records attributed to Irit Nowik.

3 recordsLinked to original sources

arXiv2023

How Advance Sales can Reduce Profits: When to Buy, When to Sell, and What Price to Charge

A consumer who wants to consume a good in a particular period may nevertheless attempt to buy it earlier if he is concerned that in delaying he would find the good already sold. This paper considers a model in which the good may be offered in two periods; the period in which all consumers most value the good (period 2), and an earlier period (period 1). Examining the profit-maximizing strategy of the firm under unbounded demand, we find that even with no cost of making the product available early, the firm does not profit, and usually loses, by making the product available early. Interestingly, the price that maximizes profits induces all arrivals to occur early, or all arrivals to occur late, depending on the parameters. The firm would not set a price which induces consumers to arrive in both periods. In particular, if the firm controls the penalty for arriving early, then it should set a high penalty so that no one arrives early. The Nash equilibrium behavior of consumers, when deciding if and when to arrive is more complicated than one may suppose, and can generate some unexpected behavior. For example, when there is unbounded demand, most potential consumers decide not to arrive at all. Additionally, the arrival rate may decline with the surplus a person gets from buying the good. Surprisingly, we find that an increase in the number of units for sale increases the number of consumers who arrive early. Moreover, we find that the profit-maximizing price increases with the number of units offered for sale. This too is unexpected as an increase in supply often results in price reduction. In our case, an increase in the number of units on sale also increases demand, and the seller may profit by increasing the price. In the single-unit case, we give closed solutions for the equilibrium customer behavior and profit-maximizing firm strategy and conduct sensitivity analysis.

econ.GN↗

arXiv2016

On the price of anarchy in a single server queue with heterogenous service valuations induced by travel costs

This work presents a variation of Naor's strategic observable model (1969), by adding a component of customer heterogeneity induced by the location of customers in relation to the server. Accordingly, customers incur a travel cost which depends linearly on the distance of the customer from the server. The arrival of customers with distances less than x is assumed to be a Poisson process with rate lambda(x)=int_0^x h(y)dy<\infty, where h(y) is a nonnegative intensity function of the distance y. In a loss system M/G/1/1 we define the threshold Nash equilibrium strategy x_e and the optimal social threshold strategy x^*. We show that if the rate of arriving customers is bounded then PoA converges to 1 when x_e \to\infty, i.e., in the limit there is no difference between the social and equilibrium optimal benefits. The rest of the paper is dedicated for the case in which the rate of arriving customers is unbounded. We develop an explicit formula to calculate lim_{x_e\to \infty}PoA when it exists. We present sufficient conditions for the limit to exist and for the existence of a simple formula for calculating it. We prove that if the relation between two intensity functions converges to a positive constant, then the corresponding limits of PoA coincide. If, on the other hand, one intensity function is larger than the other from some point on, then under certain conditions the limit of PoA (if exists) will be larger for the larger intensity function. For all intensity functions h, we prove that if h converges to a constant then PoA converges to 2, and that if from some point on h decreases (increases) monotonically then the limit of PoA, if exists, is smaller (larger) than 2. In a system with a queue we prove that the price of anarchy may be unbounded already in the simple case of uniform arrival, namely h~c, where c>0.

math.OC↗

arXiv2016

Blotto Games with Costly Winnings

We introduce a new variation of the m-player asymmetric Colonel Blotto game, where the n battles occur as sequential stages of the game, and the winner of each stage needs to spend resources for maintaining his win. The limited resources of the players are thus needed both for increasing the probability of winning and for the maintenance costs. We show that if the initial resources of the players are not too small, then the game has a unique Nash equilibrium, and the given equilibrium strategies guarantee the given expected payoff for each player.

math.OC↗