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Horse trading game with single seller:-
Find the core of the variant of the horse trading game in which there is a single owner, whose valuation is less than the highest valuation of the non owners.
If you have studied economics you know that this outcome is the same as the "competitive equilibrium". The theories differ, however. The theory of competitive equilibrium assumes that all trades take place at the same price. It defines an equilibrium price to be one at which "demand" (the total number of nonowners whose valuations exceed the price) is equal to "supply" (the total number of owners whose valuations are less than the price).
This equilibrium may be justified by the argument that if demand exceeds supply then the price will tend to rise, and if supply exceeds demand it will tend to fall. Thus in this theory, "market pressures" generate an equilibrium price; no agent in the market chooses a price.
By contrast, the coalitional game we have studied models the players' actions explicitly; each group may exchange its horses and money in any way it wishes. The core is the set of actions of all players that survives the pressures imposed by the trading opportunities of each possible group of players. A uniform price is not assumed, but is shown to be a necessary property of any action in the core.
Find the matchings produced by the deferred acceptance procedure both with proposals by X's and with proposals by Y's for the preferences given in Figure.
Under what conditions on m and n do you know that one of the players has a strategy that guarantees a win? Can you determine which player can guarantee a win? If so, provide some logic or a proof.
Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
Compare the BNE prices if Firm l's realized cost is high with the equilibrium prices in the game where it is common knowledge that Firm 1 has high marginal cost (cH).
Show that the strategy pair is not a subgame perfect equilibrium: find a player who can increase her payoff in some subgame. How much can the deviant increase its payoff?
Consider a two-stage game where firms invest in cost-reducing R&D in the first stage and set prices in the second stage. Classify and explain the R&D investment strategy in case of s = 0 according to the general taxonomy of business strategies
What is the probability that Marie will be ranked number one after this year? What is the probability that Marie will win all 4 games this year against Jan?
Write the Budget Constraint of the ministry as a function of the annual budget m, the km of roads x1, the added tons to the port x2, and the costs p2, b and g.
the seller of durable goods whom we have met before.this time he is selling to three potential consumers h m l remember
Prove that (0,0) is a Nash equilibrium. - Graph the players' best responses as a function of each other's strategies. - Find all of the other Nash equilibria.
Draw this game in extensive form. - Using a matrix representation, find all the pure-strategy Bayesian Nash equilibria for this game.
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