請讀完附加檔案并寫下心得

1、賽局- 請讀完附加檔案並寫下心得 並上傳到BB 期末考作業(yè)=What is the Nash equilibria in this given attached file.期末考作業(yè)=What is the Nash equilibria in this given attached file.In this case, the Cooperation Game from the Lecture Note is an example in which both players view the strategies as strategic complements, though both p

2、layers prefer that the other be more aggressive (i.e. do more work). 在這一個案中，課堂筆記里的合作博弈是一個的例子，該例子中博弈參與各方都將策略視為互補策略，雖然他們希望對方付出更多努力。Is it possible to plausibly modify the Cooperation Game so that one of the players prefers the other to be less aggressive, while keeping the strategic complementarity? St

3、rategic complementarity in this game means that each worker wants to work hard if the other works hard but not otherwise. In the original Cooperation Game, the reason for this is that each worker is only willing to put in effort if that will lead to the job getting done. Thus, you prefer that the ot

4、her player works harder since then more of the task gets done. But another natural reason to work only if the other player works is to avoid looking bad to the boss. In that case, you will prefer that the other player works less since then you will look relatively better. Let's try to create a v

5、ery simple game based on this idea. (Having a simple game, obviously, simplifies the analysis in the second part.) 這段討論了是否存在一種調(diào)整合作博弈的方法，使得合作博弈的各方都希望對方付出更少的努力，同時又能確保策略的互補性。他首先解釋了原本的合作博弈的表現(xiàn)及其背后原因，接著提出了另一種可能的表現(xiàn)形式及其原因，來說明對原來的合作博弈的調(diào)整方法。接下來作者將舉例說明這種方法。 Solution  The Game: "Working with a Sl

6、acker". Two workers. Each has a simple choice, Work or Not. If both Work the job gets done well, but if one or both of them do not work then the job gets done poorly. Worker A (Alice) only wants to work if doing so will lead to a well-done job. In particular, having a well-done job is "wor

7、th 10" and working "costs 5". Worker B (Bob) only wants to avoid looking bad. In particular, while working "costs 5", being the only one not to work "costs 10". (Note that, holding her own action fixed, Alice prefers for Bob to work harder whereas, holding his acti

8、on fixed, Bob prefers that Alice work less. 1 ) Putting this together, we get the payoff matrix 作者舉了這樣一種博弈情況，A參與工作只是想要將工作做好，而B參加工作只是希望保持好形象。因此，對A來說，工作做好可得到10，因為工作做好事A的目標，效用大,A參與工作花費5;對B來說，參加工作花費5，而不工作將花費10，因為不工作B將會使形象受損，沒有達到它的目標，因此對他而言損失比參加工作更大。這種情況下，A會希望B付出更多努力，而B著希望A付出更少的努力。 (b) Nash equilibr

9、ia given simultaneous moves. Clearly, (WORK, WORK) and (NOT, NOT) are Nash equilibria. What about mixed strategies? By working, Alice is "risking 5 (payoff -5 rather than 0) to gain 5 (payoff 5 rather than 0)" so for her to be indifferent Bob must work 50% of the time. Similarly, by workin

10、g Bob is "risking 5 (payoff -5 rather than 0) to gain 5因此，雙方都參與工作或都不工作將達到那時均衡的博弈結(jié)果。都工作，A得到5而B只損失5，都不工作，A沒有損失，而B也沒有損失。雙方損失的總數(shù)為0。但如果只有一個人工作，比如A工作B不工作，A將損失5且B損失10，總共損失15，A不工作而B工作，A無損失而B將損失5，總損失為5。如下面這個矩陣：In the Practice Final and in the Lecture Note on Strategic Substitutes and Complements, I rout

11、inely refer to games in which "player A wants player B to be more aggressive", etc. This means that, holding player A's action fixed, player A is never worse off (and sometimes better off) when player B chooses a higher ("more aggressive") strategy. 將A的策略固定的話，如果B選擇積極工作，那么A將永遠

12、不會有損失，甚至還有可能獲利。 (payoff -5 rather than -10)" so he is indifferent when Alice works 50%. So, is the (only) mixed-strategy equilibrium. We can also see the three equilibria by drawing the players' reaction curves. equilibria given sequential moves. When Alice goes .first: As the follower

13、, Bob's strategy is determined by his reaction curve: WORK if Alice WORKs and NOT if Alice NOTs. Given this, Alice chooses to WORK since she prefers (WORK, WORK) over (NOT,NOT). When Bob goes first: As the follower, Alice's strategy is determined by her reaction curve: WORK if Bob WORKs and

14、NOT if Bob NOTs. Given this, Bob chooses NOT since lie prefers (NOT,NOT) over (WORK, WORK). 對B來說，如果A選擇工作，他也選擇工作，A不工作，他也不工作。對A來說也如此。但如果A先選擇，他將選擇工作，因為兩人都工作隊A最有利。如果B先選，他將選擇不工作，因為兩人都不工作對B最有利。Note: to be fully correct, you must specify a player's action at every one of his information sets. For examp

15、le, when Alice is leader Bob has two information sets: (1)Alice WORKs and (2) Alice NOTs. In equilibrium, we don't observe what Bob was planning to do if Alice didn't work, but his plan of action in that unrealized event is an important part of the equilibrium. (d) Preferences over moving fi

16、rst vs. last. For Alice: When Alice moves first, we have the outcome (WORK, WORK), whereas when Alice moves last we have the outcome (NOT, NOT). Thus, moving first is better than moving last. For Bob: When Bob moves first, we have the outcome (NOT, NOT), whereas when Bob moves last we have the outco

17、me (WORK, WORK). Thus, moving first is better than moving last. 如果雙方的行動分先后順序，結(jié)果是A和B都會偏好首先行動，因為這樣可以得到他們最想要的均衡結(jié)果。The results of the previous paragraph are to be expected. Take Alice: since Bob views the strategies as strategic complements and Alice wants Bob to work more, we know that she will tend to work more as the leader than when moving simultaneously. This makes Bob worse off and explains why he prefers not to be the follower. Similarly. since Alice views the strategies as strategi