BASIC MODEL. In the previous chapters, I have developed a concept that aims at explaining the evolution of dynamic capabilities in technology-based new ventures by linking the strategic management framework to entrepreneurial learning and organisational development and change. In the course of this effort, I have derived various hypotheses that support this concept and the underlying approaches and theories. To denote the links between the concept and the different hypotheses, I provide a summary of the different findings from the theoretical part of this study in this third chapter.
BASIC MODEL. We follow Xxxxx and Xxx (2013), who extend the concept of Perfectly Coalition-Proof-Xxxx Equilibrium (PCPNE) advanced by Xxxxxxxx et al. (1987) to settings in which overlapping coalitions may coexist. We show this extension in Appendix A. It employs the perfectly coalition-proof concept to the sets of players produced by the union of intersecting (i.e., overlapping) sets of players. Suppose that N = {1, 2,3} denotes the set of all players. In addition to N , the subsets of the set of all players are the singletons, {1},{2},{3} and the pairs {1, 2} , {1,3} , {2,3} . The standard coalition-proof concept is applicable to all coalitional structures except to the overlapping ones, in which one nation is a hub. The extended concept of Xxxxx and Xxx (2013) is applicable to the overlapping coalitional structures: it is employed over the union of the overlapping bilateral coalitions; namely the set {1, 2,3} . Consider, for example, the coalitional structure in which nation 1 is a hub and nations 2 and 3 are spokes; that is, the coalitions{1, 2} and{1,3} coexist in equilibrium. The Xxxx equilibrium for this structure is coalition-proof if and only if there is no individual nor collective incentive to deviate; that is, player 1 has no incentive to exit either coalition, and players 2 and 3 have no incentives to exit their respective coalitions in order to stand alone or to form the bilateral coalition {2,3} . The latter is one of the possible self-enforcing sub-coalitions that can be produced from the set {1, 2,3} . The game considered here is a strategic network formation game. We formulate a multistage game, in which the first stage is a participation stage. If the joint R&D agreements prohibit transfers, the game contains two stages: following the participation stage, there is a contribution stage. If the joint R&D agreements allow transfers, the game also includes a third stage in which coalitions implement transfers. Formally, the participation stage can be described as follows. For a game where N = {1, 2,3} , a pointing game Γ is a list (N ,(Si ) ,Ui ) , where S = {0,1}N \{i} = {0,1}×{0,1} for i∈N each i ∈ N (a representative element si = {sij , sik }∈ Si describes the countries that country i is pointing towards to initiate an agreement, and sij = 1 means that country i selects country j while sij = 0 means that country i does not select country j ) and Ui (si , s−i ) = ui ({i, j} ⊂ N : sij = s ji = 1) for each i ∈ N . We later extend the model to allow for a ...
BASIC MODEL. The Xxxxxxxxx model is based on a single period setting. Suppose we invest X0 amount of money in an asset at time t = 0 and after a period of time, we sell the asset at price X1. Here, we denote the ratio R = X1 X0 as the return on the asset. Then, the rate of return on the asset is defined as µ = X1 − X0 X0 = R − 1. Thus, we have X1 = RX0 = (1 + µ)X0. Now consider the case with n securities. Let X0 be the initial amount of money we are holding at time t = 0. We wish to distribute this amount of money into n asset and the amount that we assign to asset i is X0i = uiX0 where ui denotes the i=1 fraction of investment in asset i, so Σn ui = 1. Let the total return on asset i be Xx and then the payoff from this portfolio after a period of time is n n X1 = Σ RiuiX0 = X0 Σ Riui i=1 i=1 so the total return R is Σ
