Hipótesis específicas

Strategy: The algorithm employed by the bidder in making their bidding decisions. This algorithm is either the lexicographic, straightforward, or (in the case of the IFA mechanism) complex strategy. These strategies are outlined in Section 2.3.

1Complete scale information can be found at:

https://github.com/logantner/FCC-Incentive-Dissertation/

Type: Each bidder’s interaction with the market is largely dictated by their type, which loosely specifies their resources and breadth of value across all products. These types are as follows:

• National bidders: These have the largest budgets of all the bidder types, and have value for products across all regions and localities.

• Regional bidders: These have smaller budgets than national bidders, and have value for products across all localities within a specific region.

• Local bidders: These have the smallest budgets, and their value for products is limited to a small number of localities within a specific region.

• Opportunistic bidders: These are very similar to national bidders, having value for products spanning all regions. However, opportunistic bidders have only a fraction of the budget of their national counterparts. They are analogous to smaller firms looking to participate in the auction for investment or speculative purposes.

The bidder type is a higher level attribute, influencing values of lower level attributes such as budget and coverage distributions. In this sense, it is largely an organizational tool.

Coverage Distribution: Bidder type broadly determines regions and localities bidders can have value. The value coverage distribution determines how much products from these allowed sectors will be valued. For example, if a regional bidder has a value coverage of 60%, then they will be assigned (roughly) 60% of the products from their assigned region to have positive value. The coverage itself is drawn from a uniform distribution whose limits depend on both the bidder type and market scale. These values can be found in Table 2.1.

In the case of national, opportunistic and regional bidders, the value coverage is drawn and used to determine the quantity of valued products. These products are then drawn from the relevant item pool (all items for national and opportunistic, the assigned region for regional) using a weighted distribution with respect to the expected value of each item.

Local bidders are a special case. Instead of sampling a region, they sample one or more localities from an assigned region as their item pool. Their coverage is always uniformly drawn between 0% and 100%, with a minimum item count of 1, after which they sample from their item pool like normal.

Maximum Localities (local types only): As mentioned when discussing coverage, local bidder types sample one or more localities in determining value draws. The number of localities is drawn uniformly between one and the maximum number of localities, which is itself a function of the market scale. Because local bidders always randomize coverage uniformly between 0% and 100% of their item pool, Table 2.1 presents the locality range for local bidders instead of their coverage range.

Maximum Valued Licenses: In addition to being assigned products of value, bidders will additionally be assigned a number of valued licenses within these products. This value is drawn uniformly between a single unit and a maximum number of licenses. This maximum number depends on the bidder type and the market scale, but is also subject to a binary treatment effect. Each row of table 2.1 displays the two values that a bidder type within a scale may assume, depending on the treatment. For example, opportunistic bidders in a national market will have value for up to two licenses of each product in the lower demand treatment, and up to four licenses of value in the higher demand treatment. The maximum number of licenses is always capped at the supply of a product, where supply would be a limiting factor.

Value Distribution: Once licenses of value are determined, bidders are assigned random value draws for each of these licenses. A value, V , is drawn from a uniform distribution as

V ∼ U (µ −√

3σ, µ +√ 3σ)

The expected value, µ, is fixed to the product.² The distribution’s width, on the other hand, depends on σ and is a binary treatment effect across simulations. Its value will either be one third of the product’s mean value, or 2% of the mean value. The intention is to create environments which differ significantly in competitive engagement.

When a bidder has value for more than one license within a product, these values are drawn independently from the same distribution. Afterward, they are sorted from highest to lowest value to guarantee monotonicity of values. These are base values, and have not yet factored details such as expected impairment.

2Complete product information can be found at:

https://github.com/logantner/FCC-Incentive-Dissertation/

Table 2.1: Bidder information by type and market scale.

Each cell under max valued licenses contains two values representing the two possible valued license counts based on the treatment implemented. Local bidders always drew coverage between 0% and 100%, so coverage indicates the maximum number of localities that local bidders may select from.

Impairment Value Discount: The value that a bidder is assigned for each value assumes that the bidder applies no discount to the product based on its impairment. In reality potential buyers may respond to impairment very differently based on their needs, and so are assigned unique impairment discount rates that are applied to their product valuations:

Bidder Value = (Base Value) · (Expected impairment) · (Impairment discount) The impairment discount rate is randomly drawn from a uniform distribution specific to the product, as discussed in the previous section.

Budget and Budget Distribution: Each bidder is assigned a budget when generated.

This budget is drawn from a uniform distribution, whose limits are a function of bidder type and market scale. These values can be found in Table 2.1.

Starting Eligibility: Finally, each bidder is assigned a starting eligibility as a function of their budget. Bidders receive a unit of starting eligibility for each $2500 of budget, rounded down. This applies to all bidders in all market scales.

Reserve Eligibility Status: This includes an indicator of whether the bidder is reserve eligible and may therefore bid on reserve products after the reserve split. National bidders are never reserve eligible, while opportunistic, regional and local bidders are always reserve eligible. Reserve eligible bidders treat the value of reserve products identically to their non-reserve counterparts.