## 经济代写|博弈论代写Game Theory代考|ECON3050

2022年12月29日

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## 经济代写|博弈论代写Game Theory代考|FAIRNESS PROPERTIES

In the previous sections, we defined and used three bargaining game solution methods: egalitarian, Raiffa, and Nash. In this section, we describe a variety of fairness properties for solution methods and identify which of these properties apply to our three methods. This provides a way to choose a solution method based upon general principles. From a modeling perspective, the formal properties we define give us a way of modeling the real-world concept of fairness, and the characterization theorems are the results of our mathematical analysis of our models in light of these properties.

We emphasize here the difference between a solution for a particular bargaining game and a solution method that can be used to determine solutions for any bargaining game in some large collection of bargaining games. The former could be obtained in an ad hoc manner based on biases or special circumstance, whereas the latter suggests uniformity of treatment. When we discuss fairness properties for a solution method, we mean that property applies to the method regardless of the bargaining game.

Our first fairness property suggests that players should not settle for an outcome if a different outcome is het.ter for at. lesst one player without heing worse for any player. By better we mean that the outcome $o_a$ dominates [resp., strongly dominates] the outcome $o_b$, which occurs if and only if the payoff pair $x=\left(u_1\left(o_a\right), u_2\left(o_a\right)\right)$ dominates [resp., strongly dominates] the payoff pair $x-\left(u_1\left(o_b\right), u_2\left(o_b\right)\right)$. Formally,

Definition 4.3.1. An outcome is efficient if there is no outcome that dominates it. A solution method is efficient on a set of bargaining games if it always chooses an efficient outcome.

Our second fairness property suggests that no player should agree to an outcome that is worse than having no agreement.

Definition 4.3.2. An outcome is rational if it is not dominated by the disagreement outcomē. A solution method is rational if it always chooses a rảtional outcomé.

Our third fairness property suggests that if all players have the same opportunities, then they should share equally.

## 经济代写|博弈论代写Game Theory代考|SEQUENTIAL GAMES

In the early $2000 \mathrm{~s}$, media-streaming products were introduced by a few companies to compete with cable TV. Within a few years, several other companies joined the market with similar products. Bierman and Fernandez [12] created a model of competing software companies developing new products. Here we adapt their model for a fictitious scenario in which one company is attempting to clone another’s media streaming device in order to capture market share.

In this scenario, we consider PlumProducts and SeeTV to be the players. We next need to determine the chronology of player actions. To start, PlumProducts can choose to include or not include restraining clauses in its engineers’ contracts (Restrain or Open). In either case, SeeTV will later choose to enter or not enter the market with its own product (In or Out). Finally, if SeeTV chooses to enter the market, PlumProducts will choose to be Aggressive or Passive with its marketing. This chronology determines the possible terminal histories, outlined in Table 5.1. The sequential nature of the game is nicely captured in the game tree illustrated in Figure 5.1. Table $5.2$ lists non-terminal histories and the player who acts at each subhistory.

In the game tree, the shaded circles, called nodes, correspond to non-terminal histories. For example, the node labeled “D5” corresponds to the non-terminal history “Open, In.” The label above the D5 node indicates that it is PlumProducts’ turn to act. PlumProducts can choose to either be Aggressive or Passive, as indicated by the labels on the line segments, called edges, emanating from the D5 node to the right. In the former case, the terminal history is “Open, In, Aggressive.” In the latter case, the terminal history is “Open, In, Passive.”

To continue modeling this scenario, we need to quantify the various financial components. How we do this will affect the fidelity and flexibility of our model. Here we will choose values that are not supported by data, but seem reasonable for the scenario. This makes our model flexible, but reduces the fidelity.

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## MATLAB代写

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