a) Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied.
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A: Given, λ11=λ=0λ12=10λ21=1 We have to write the optimal decision rule.
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- Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…Draw a decision tree given problem below. A businessman must decide whether to open a new mini grocery branch or simply extend the number of hours of its operation on its existing branch with a payoff of Php150,000. According to his friend, demand at a new location can either be low or high, which he probabilities are estimated to be 35% and 65%, respectively. If a new branch is opened and demand proves to be high, the businessman may choose to operate 24hrs (payoff is Php350, 000) or to operate 12hrs (payoff is Php200,000). If a new branch is opened and demand proves to be low, there is no need to operate on a 24-hr basis but instead, they will just stick to 12-hr operation with payoff of Php100,000 or enhance marketing strategy through advertising. Projected response to advertising may either be favorable or not favorable, with estimated probabilities of 40% and 60%, respectively. If demand is favorable, the payoff grows to Php310,000 and if the response in unfavorable, the payoff is…Problem 17.6. There were n Immortal Warriors born into our world, but in the end there can be only one. The Immortals’ original plan was to stalk the world for centuries, dueling one another with ancient swords in dramatic landscapes until only one survivor remained. However, after a thought-provoking discussion probability, they opt to give the following protocol a try: (i) The Immortals forge a coin that comes up heads with probability p. (ii) Each Immortal flips the coin once. (iii) If exactly one Immortal flips heads, then they are declared The One. Otherwise, the protocol is declared a failure, and they all go back to hacking each other up with swords. One of the Immortals (Kurgan from the Russian steppe) argues that as n grows large, the probability that this protocol succeeds must tend to zero. Another (McLeod from the Scottish highlands) argues that this need not be the case, provided p is chosen carefully. (a) A natural sample space to use to model this problem is fH; T g n…
- The Manhattan Tourist Problem (1) Given setting in Figure 6.4, calculate exact number of different paths by dynamic programming. (2) For a general setting, i.e., from source(0,0) to sink (n, m), how many different paths by dynamic programming?1 4 3 3 4 1 0 4 3 N 5 1Given a symmetric propagationmatrix W and the general initial condition c^0' = 0 or Ai = 0. If option x*(x* G Di) is in the global optimum, then c\ {x*) must satisfy the followinginequality,^«)<f+y^i4 k ) i ^ .1-)a.Find the starting solution of this transportation model by Least Cost Method. (Unit transportation costs are given in the table) 2-)Then find the optimal solution of this transportation model by Stepping Stone Method. D1 D2 D3 D4 Supply M1 16 24 14 11 25 M2 21 18 17 9 30 M3 15 13 21 14 40 Demand 25 25 20 25
- Write a python code of this problem Problem Statement Assume that there are two teams and they are team attacker and team defender. Therefore, at a state of the game one agent in each team is left alive respectively. Here, the defender is given a lifeline called HP which will be assigned randomly. Furthermore, the attacker agent will try to give maximum negative HP to the defender agent to decrease his(d) chances of survival in the game. On the other hand, the defender agent will try to protect himself by receiving the lowest negative HP possible from the attacker agent. Furthermore, the attacker can have a choice from a number of bullets from his gun and the optimal moves will cost a certain maximum negative HP (chosen from randomly assigned values within the range of minimum and maximum negative HP). Here, are the following things you need to do using Alpha-Beta Pruning algorithm: Sample Input 1: Enter your student id: 17301106 Minimum and Maximum value for the…Consider the following model of trade between Home and Foreign. Assume throughout that those two countries are the only two countries in the world, at least for purposes of trade. There are two goods: Corn and Radio. Consumers always spend one-third of their income on Corn and the remainder on Radios. The only factor of production is labour. Each home country worker can produce 2 units of Corn or 3 units of Radios per unit of time, while each foreign worker can produce 2 units of Corn or 4 units of Radios per unit of time. There are 30 workers in Home and 60 workers in Foreign. Draw the production possibility frontier for each country (put Corn on the vertical axis and Radios on the horizontal axis).South Africans and Botswanaans enjoy Chakalaka and Beer. Suppose that these are the only two products they consume and produce with Chakalaka being relatively more labour intensive and Beer being relatively more capital intensive in the production process ( αb=0.8 and αc=0.2). Suppose that, as a result of the Southern African Customs Union, all impediments or barriers to trade are lifted, such that these countries can freely trade both goods without any costs. Assuming that an Entrepreneur knows the price of both these goods and both goods are produced, using the Learner diagram describe how the entrepreneur chooses the cost-minimising combinations of inputs in the production of both goods based on the neoclassical trade theory.
- A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below. (a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.Q.1 We have three tasks A, B, C, that need to be assigned to two workers X and Y . We encode this problem in propositional logic by using atomic propositions tw that are true when task t is assigned to worker w. For example, if AX is true then task A is assigned to worker X. A valid solution to the problem must satisfy two constraints: (1) Every task is assigned a worker; and (2) Task B cannot be assigned the same worker as tasks A or C. (b) Write out a propositional logic formula in Conjunctive Normal Form (CNF) for which the satisfying valuations are exactly the correct assignments of machines to tasks. Clearly label the parts of the formula to describe what constraint they are encoding.Computer Science Consider the demand and supply system p = ad +bdqd +ud p = as +bsqs +us with the equilibrium condition qd = qs = q. The parameters bd and bs are −2 and 1.5, respectively. Find the parameters ad and as are such that q = 5 and p = 10. Throughout this question use N = 100, and set the random seed to 14022022. The variable ud has a standard deviation of 3. All randomly generated variables have a mean of zero and are normally distributed unless something else is specified. All Monte Carlo studies should be done with 10,000 repetitions. Part a. Illustrate the supply and demand curves in a graph, together with a sample of simulated price and quantity data. Provide an additional graph where you have included the OLS estimated line of demand equation above. Are your estimates close to the true values of ad and bd ? Solve the question in Python language on Jupyter notebook.