Homework answers / question archive / 1) Consider a two player Bayesian game with the following payof matrix R s p R s p 1 (81), 1 (82) 1 (81) + 10, 9 (82) - 10 1 (81) - 10, h (82) + 10 9 (81) - 10, 1 (82) + 10 9 (81), 9 (82) 9 (81) + 10, h (82) - 10 h (81) + 10, 1 (82) - 10 h (81) - 10, 9 (82) + 10 h (81), h (82) where 8i E {0, 1, 2} is privately known by player i and 1 (0) = 1, 1 (1) = 1 (2) = sian Nash equilibrium of this game

1) Consider a two player Bayesian game with the following payof matrix R s p R s p 1 (81), 1 (82) 1 (81) + 10, 9 (82) - 10 1 (81) - 10, h (82) + 10 9 (81) - 10, 1 (82) + 10 9 (81), 9 (82) 9 (81) + 10, h (82) - 10 h (81) + 10, 1 (82) - 10 h (81) - 10, 9 (82) + 10 h (81), h (82) where 8i E {0, 1, 2} is privately known by player i and 1 (0) = 1, 1 (1) = 1 (2) = sian Nash equilibrium of this game

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1) Consider a two player Bayesian game with the following payof matrix R s p R s p 1 (81), 1 (82) 1 (81) + 10, 9 (82) - 10 1 (81) - 10, h (82) + 10 9 (81) - 10, 1 (82) + 10 9 (81), 9 (82) 9 (81) + 10, h (82) - 10 h (81) + 10, 1 (82) - 10 h (81) - 10, 9 (82) + 10 h (81), h (82) where 8i E {0, 1, 2} is privately known by player i and 1 (0) = 1, 1 (1) = 1 (2) = sian Nash equilibrium of this game. Verify that the strategy profle you identifed is indeed a Bayesian Nash equilibrium. 2. There are two identical objects and three potential buyers, named 1, 2, and 3. Each buyer only needs one object and does not care which of the identical objects he gets. The value of the object for buyer i is Vi where (V1, V2, V3) are independently and uniformly distributed on [0, 1]. The objects are sold to two of the buyers through the following auction. Simultaneously, each buyer i submits a bid bi, and the buyers who bid one of the two highest bids buy the object and pay their own bid. (The ties are broken by a coin toss.) That is, if bi > bj for some j, i gets an object and pays bi, obtaining the payof of Vi - bi; if bi < bj for all j, the payof of i is 0. (a) (5 points) Write this as a Bayesian game. (b) (20 points) Compute a symmetric Bayesian Nash equilibrium of this game in increasing diferentiable strategies. (You will receive 15 points if you derive the correct equations without solving them.) 3. A state government wants to construct a new road. There are n construction frms. In order to decrease the cost of delay in completion of the road, the government wants to divide the road into k 0. The cost of constructing a segment for frm i is ci/k where (c1,...,cn) are independently and uniformly distributed on [0, 1], where ci is privately known by frm i. The government hires the frms through the following procurement auction. k + 1st-price Procurement Auction Simultaneously, each frm i submits a bid bi and each of the frms with the lowest k bids wins one of the segments. Each winning frm is paid the lowest k + 1st bid as the price for the construction of the segment. The ties are broken by a coin toss. 1 The payof of a winning frm is the price paid minus its cost of constructing a segment, and the payof of a losing frm is 0. For example, if k = 2 and the bids are (0.1, 0.2, 0.3, 0.4), then frms 1 and 2 win and each is paid 0.3, resulting in payof vector (0.3 - c1/2, 0.3 - c2/2, 0, 0). (a) (10 points) For a given fxed k, fnd a Bayesian Nash equilibrium of this game in which no frm bids below its cost. Verify that it is indeed a Bayesian Nash equilibrium. (b) (10 points) Assume that each winning frm is to pay ( E (0, 1) share of the price to the local mafa. (In the above example it pays 0.3( to the mafa and keep 0.3(1 - () for itself.) For a given fxed k, fnd a Bayesian Nash equilibrium of this game in which no frm bids below its cost. Verify that it is indeed a Bayesian Nash equilibrium. (c) (5 points) Assuming that the government minimizes the sum of Cp and the total price it pays for the construction, fnd the condition for the optimal k for the government in parts (a) and (c). Show that the optimal k in (c) is weakly lower than the optimal k in (a). Briefy interpret the result. [Hint: the expected value of the k + 1st lowest cost is (k + 1) / (n + 1).] 4. Stage Game: Alice and Bob simultaneously choose contributions a E [0, 1] and b E [0, 1], respectively, and get payofs UA = 2b - a and UE = 2a - b, respectively. (a) (5 points) Find the set of rationalizable strategies in the Stage Game above. (b) (10 points) Consider the infnitely repeated game with the Stage Game above and with discount factor 5 E (0, 1). For each 5, fnd the maximum (a*, b*) such that there exists a subgame­perfect equilibrium of the repeated game in which Alice and Bob contribute a* and b*, respectively, on the path of equilibrium. (c) (10 points) In part (b), now assume that at the beginning of each period t one of the players (Alice at periods t = 0, 2, 4,... and Bob at periods t = 1, 3, 5,...) ofers a stream of contributions ba = (at, at+1,...) and bb = (bt, bt+1,...) for Alice and Bob, respectively, and the other player accepts or rejects. If the ofer is accepted then the game ends leading the automatic contributions ba = (at, at+1,...) and bb = (bt, bt+1,...) from period t on. If the ofer is rejected, they play the Stage ( ) Game and proceed to the next period. Find (aA, bA), (aE, bE), and a, b b b such that the following is a subgame­perfect equilibrium: s* : When it is Alice's turn, Alice ofers (aA, aA,...) and (bA, bA,...) and Bob accepts an ofer (ba,bb) if and only if (1 - 5) [2at - bt + 5 (2at+1 - bt+1) + ... ] 2 2aA - bA. When it is Bob's turn, Bob ofers (aE, aE,...) and (bE, bE,...) and Alice accepts an ofer (ba,bb) if and only if (1 - 5) [2bt - at + 5 (2bt+1 (- a ) t+1) + ... ] 2 2bA - aA. If there is no agreement, in the stage game they play a, b . bb Verify that s* is a subgame perfect equilibrium for the values that you found. (If you fnd it easier, you can consider only the constant streams of contributions ba = (a, a, . . .) and bb = (b, b, . . .).) 

 

Question:
Please assist with any thoughts on the below items (1 and 2)

 

1. Systems development life cycles are crucial to integrate for most, if not all IT based projects. There are various different SDLC models, but all of them essentially accomplish the same task in promoting consitent workflow, progress, and efficiency on IT projects.

In my current work as a software engineer, I work in the agile scrum SDLC model. This is the model that I would also reccomend for GGFRT to follow. In agile, IT projects are divided into ~2 week long sprints, containing meetings at the beginning of the sprint to plan, every day to keep everyone on the same page, and typically a meeting at the end of a sprint to view it retrospectivly. For example, at the organization I work at, we have multiple different projects with multiple different teams working all in conjunction together. The daily meetings keeping everyone of different projects synchronous helps to keep everyone organized and on the same page. This is just one example of why GGFRT should implement the agile scrum work methodology, because as we know GGFRT plans to initiate multiple IT projects at once, so having everyone communicate regularly would help prevent many obstacles along the way.

 

 

 

2. From the research you conducted on the System Development Life Cycle (SDLC) models, identify which model you would recommend for the IT organization at GGFRT?  Relate your choice to one of the strategic objectives of GGFRT and thoroughly explain your answer.  In addition, please discuss potential challenges to the successful implementation of the model.

The SDLC Agile Project Management Model is recommended for GGFRT to adopt; specifically, as it relates to accomplishing their 1st and 3rd strategic objectives.  Both objectives are centered around improving IT systems and customer satisfaction. The Agile Project Management Model aims to incorporate the following principles:

Customer Satisfaction
Collaboration
Reviews at regular intervals
Sustainable development throughout the SDLC
Receptive to change
Independent teams working on all aspects of the project(s).
Technical excellence
Motivation focused
The Agile model promotes a collaborative environment that enables the developer and customers to make efficient decisions quickly and appropriately, (Usman, Ogwuleka 2018).  This model is ideal for GGFRT based on the multiple systems that require development or modifications along with the need for integration across the various systems.  Additionally, some of these systems are designed to support direct customer involvement, with the intent of improving the overall level of service GGFRT can offer its customer base.

Some potential challenges to the successful implementation of the Agile model include potential inexperience of staff, particularly with the programmers, a lack of clarity when it comes to customer expectations, mediocre documentation, and a clear understanding of the level or work and time that will be needed to successfully complete the projects.

 

2. From the research you conducted on the System Development Life Cycle (SDLC) models, identify which model you would recommend for the IT organization at GGFRT?  Relate your choice to one of the strategic objectives of GGFRT and thoroughly explain your answer.  In addition, please discuss potential challenges to the successful implementation of the model.

The SDLC Agile Project Management Model is recommended for GGFRT to adopt; specifically, as it relates to accomplishing their 1st and 3rd strategic objectives.  Both objectives are centered around improving IT systems and customer satisfaction. The Agile Project Management Model aims to incorporate the following principles:

Customer Satisfaction
Collaboration
Reviews at regular intervals
Sustainable development throughout the SDLC
Receptive to change
Independent teams working on all aspects of the project(s).
Technical excellence
Motivation focused
The Agile model promotes a collaborative environment that enables the developer and customers to make efficient decisions quickly and appropriately, (Usman, Ogwuleka 2018).  This model is ideal for GGFRT based on the multiple systems that require development or modifications along with the need for integration across the various systems.  Additionally, some of these systems are designed to support direct customer involvement, with the intent of improving the overall level of service GGFRT can offer its customer base.

 

2. From the research you conducted on the System Development Life Cycle (SDLC) models, identify which model you would recommend for the IT organization at GGFRT?  Relate your choice to one of the strategic objectives of GGFRT and thoroughly explain your answer.  In addition, please discuss potential challenges to the successful implementation of the model.

The SDLC Agile Project Management Model is recommended for GGFRT to adopt; specifically, as it relates to accomplishing their 1st and 3rd strategic objectives.  Both objectives are centered around improving IT systems and customer satisfaction. The Agile Project Management Model aims to incorporate the following principles:

Customer Satisfaction
Collaboration
Reviews at regular intervals
Sustainable development throughout the SDLC
Receptive to change
Independent teams working on all aspects of the project(s).
Technical excellence
Motivation focused
The Agile model promotes a collaborative environment that enables the developer and customers to make efficient decisions quickly and appropriately, (Usman, Ogwuleka 2018).  This model is ideal for GGFRT based on the multiple systems that require development or modifications along with the need for integration across the various systems.  Additionally, some of these systems are designed to support direct customer involvement, with the intent of improving the overall level of service GGFRT can offer its customer base.

 

Question:
Please assist with any thoughts on the below items (1 and 2)

 

1. Systems development life cycles are crucial to integrate for most, if not all IT based projects. There are various different SDLC models, but all of them essentially accomplish the same task in promoting consitent workflow, progress, and efficiency on IT projects.

In my current work as a software engineer, I work in the agile scrum SDLC model. This is the model that I would also reccomend for GGFRT to follow. In agile, IT projects are divided into ~2 week long sprints, containing meetings at the beginning of the sprint to plan, every day to keep everyone on the same page, and typically a meeting at the end of a sprint to view it retrospectivly. For example, at the organization I work at, we have multiple different projects with multiple different teams working all in conjunction together. The daily meetings keeping everyone of different projects synchronous helps to keep everyone organized and on the same page. This is just one example of why GGFRT should implement the agile scrum work methodology, because as we know GGFRT plans to initiate multiple IT projects at once, so having everyone communicate regularly would help prevent many obstacles along the way.

 

 

 

2. From the research you conducted on the System Development Life Cycle (SDLC) models, identify which model you would recommend for the IT organization at GGFRT?  Relate your choice to one of the strategic objectives of GGFRT and thoroughly explain your answer.  In addition, please discuss potential challenges to the successful implementation of the model.

The SDLC Agile Project Management Model is recommended for GGFRT to adopt; specifically, as it relates to accomplishing their 1st and 3rd strategic objectives.  Both objectives are centered around improving IT systems and customer satisfaction. The Agile Project Management Model aims to incorporate the following principles:

Customer Satisfaction
Collaboration
Reviews at regular intervals
Sustainable development throughout the SDLC
Receptive to change
Independent teams working on all aspects of the project(s).
Technical excellence
Motivation focused
The Agile model promotes a collaborative environment that enables the developer and customers to make efficient decisions quickly and appropriately, (Usman, Ogwuleka 2018).  This model is ideal for GGFRT based on the multiple systems that require development or modifications along with the need for integration across the various systems.  Additionally, some of these systems are designed to support direct customer involvement, with the intent of improving the overall level of service GGFRT can offer its customer base.

Some potential challenges to the successful implementation of the Agile model include potential inexperience of staff, particularly with the programmers, a lack of clarity when it comes to customer expectations, mediocre documentation, and a clear understanding of the level or work and time that will be needed to successfully complete the projects.