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p-additive games: a class of totally balanced games arising from inventory situations with temporary discounts

Ana Meca, Luis A. Guardiola, Andrés Toledo

TL;DR

It is shown that every p-additive game and its corresponding subgames have a nonempty core and the modified SOC-rule is proposed as a solution for p- additive games.

Abstract

We introduce a new class of totally balanced cooperative TU games, namely p -additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo, 2002) and contains the class of inventory cost games (Meca et al. 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character concave or convex and monotone of p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover, two characterizations of the modified SOC-rule are provided.

p-additive games: a class of totally balanced games arising from inventory situations with temporary discounts

TL;DR

It is shown that every p-additive game and its corresponding subgames have a nonempty core and the modified SOC-rule is proposed as a solution for p- additive games.

Abstract

We introduce a new class of totally balanced cooperative TU games, namely p -additive games. It is inspired by the class of inventory games that arises from inventory situations with temporary discounts (Toledo, 2002) and contains the class of inventory cost games (Meca et al. 2003). It is shown that every p-additive game and its corresponding subgames have a nonempty core. We also focus on studying the character concave or convex and monotone of p-additive games. In addition, the modified SOC-rule is proposed as a solution for p-additive games. This solution is suitable for p-additive games since it is a core-allocation which can be reached through a population monotonic allocation scheme. Moreover, two characterizations of the modified SOC-rule are provided.
Paper Structure (6 sections, 10 theorems, 30 equations)

This paper contains 6 sections, 10 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Temporary discounts on inventory problems
  4. Inventory games with non discriminatory temporary discounts
  5. $p$-additive games
  6. Modified SOC-rule

Key Result

Proposition 4.1

Let $\left\langle N,a,d,m,k,\lambda \right\rangle$ be an inventory situation with non discriminatory temporary discounts. There always exists $0<\alpha \leq 1$ such that $\lambda (S)/\lambda (N)=\alpha m_{S}^{2}/m_{N}^{2},$ for every nonempty coalition $S\subseteq N.$

Theorems & Definitions (18)

  • Proposition 4.1
  • Theorem 5.1
  • Example 5.2
  • Example 5.3
  • Proposition 5.4
  • Corollary 5.5
  • Theorem 5.6
  • Lemma 5.7
  • Proposition 5.8
  • Proposition 6.1
  • ...and 8 more